id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
800,270 | AMR-119-0066 | Several Complex Variables Problem List — Problem 69 | Is the support of $\mu$ equal to the closure of the repelling periodic orbits? | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 69
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,271 | AMR-119-0067 | Several Complex Variables Problem List — Problem 70 | Does there exist a holomorphic map $F:\mathbb{P}^k \rightarrow \mathbb{P}^k$ with a wandering Fatou component $U$, i.e. $F^n(U) \bigcap F^m(U) = \emptyset $ for all $n \neq m$? | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 70
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,272 | AMR-119-0068 | Several Complex Variables Problem List — Problem 71 | Classify the dynamics around a fixed point of a holomorphic map on $\mathbb{P}^k$
or even just defined in a neighborhood of p.
-sibony@anh.matups.fr | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 71
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,273 | AMR-119-0069 | Several Complex Variables Problem List — Problem 72 | Let $f:\mathbb{P}^2 \rightarrow \mathbb{P}^2$ be a holomorphic map of degree $d \geq 2$. Assume K is a totally invariant set. Let C denote the critical set of $f$. Assume $\overline{\bigcup_{n=1}^{\infty} f^n(C)} \bigcap K = \emptyset$. Is f hyperbolic on K? | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 72
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,274 | AMR-119-0070 | Several Complex Variables Problem List — Problem 73 | Let $H_d$ denote the space of holomorphic maps $f:\mathbb{P}^2 \rightarrow \mathbb{P}^2$ of degree d. This is a finite dimensional space parametrized by the coefficients. Does the set of $ f\in H_d$ with infinitely many attractive basins have measure zero? | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 73
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,275 | AMR-119-0071 | Several Complex Variables Problem List — Problem 74 | Let $f:\mathbb{P}^2 \rightarrow \mathbb{P}^2$ be a holomorphic map of degree $d \geq 2$ and let $\lambda_1 \leq \lambda_2$ be the Lyapunov exponents for the ergodic measure $\mu = T \wedge T$. Is $\lambda_1 >0$? | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 74
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,276 | AMR-119-0072 | Several Complex Variables Problem List — Problem 76 | Is every compact reduced analytic space biholomorphically equivalent to a
subvariety of a complex manifold? If so, can the manifold be chosen to be compact?\\
-E. L. Stout, stout@math.washington.edu | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 76
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,277 | AMR-119-0073 | Several Complex Variables Problem List — Problem 77 | Let C be a smooth cubic in $\mathbb{P}^2$. Then $\mathbb{P}^2\setminus C$
is algebraically parallellizable, but cannot be algebraically immersed in $\mathbb{C}^2$. Can it be holomorhically immersed in $\mathbb{C}^2$?
[ There are smooth cubics for which it is true . For related problems see the section called ``Stein ma... | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 77
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,278 | AMR-119-0074 | Several Complex Variables Problem List — Problem 78 | Consider the following statement: `` Let Y be a compact subset of $\mathbb{C}^2$
which lies over the circle $|\lambda|= 1$, and let U be an open
neighborhood of K, the polynomially convex hull of Y. Then there exists a finitely
sheeted Riemann surface S lying over $|\lambda| < 1$ as a branched covering such
that $S\sub... | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 78
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,279 | AMR-119-0075 | Several Complex Variables Problem List — Problem 79 | Let M be a K$\ddot{a}$hler manifold. Assume that all curvatures are between
$-a^2$ and $-b^2$. Construct nontrivial bounded holomorphic functions on M.\\
-N. Sibony, sibony@anh.matups.fr | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 79
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,280 | AMR-119-0076 | Several Complex Variables Problem List — Problem 80 | Are strongly pseudoconvex CR surfaces of real dimension 5 locally embeddable? | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 80
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,281 | AMR-119-0077 | Several Complex Variables Problem List — Problem 81 | Let $M \subset P^n$ be a compact odd dimensional CR manifold. Find conditions
on M which ensure that M bounds a complex variety.(This is well understood in
$\mathbb{C}^n$.)\\
-N.Sibony, sibony@anh.matups.fr | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 81
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,282 | AMR-119-0078 | Several Complex Variables Problem List — Problem 82 | **(New) (Liouville type assertion on CR 3-manifolds) On a CR 3-manifold
one can always define a Carnot-Caratheodory metric. A homeomorphism between
two strongly pseudoconvex CR 3-manifolds is called conformal if it maps
infinitesimal spheres with respect to a Carnot-Caratheodory metric to
infinitesimal spheres. Is a co... | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 82
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,283 | AMR-119-0079 | Several Complex Variables Problem List — Problem 83 | **(New) A diffeomorphism between two strongly pseudoconvex CR
$(2n+1)$-manifolds is called quasiconformal if its differential preserves
the underlying contact structures and distorts the CR structures boundedly.
When Hermitian metrics on the contact bundles are fixed, this distortion
can be measured by checking how sph... | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 83
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,284 | AMR-119-0080 | Several Complex Variables Problem List — Problem 84 | Let $\Omega \subseteq \mathbb{C}^n$ be a bounded domain with complete Kobayashi
metric.
Is there a constant $C = C(p) > 0$ such that if $f$ is holomorphic and $p > 0$
then for all $z \in \Omega$ and all $r > 0$ small it holds that
$$
|f(z)|^p \leq C \frac{1}{|B(z,r)|} \int_{B(z,r)} |f(\zeta)|^p dV(\zeta) .
$$
Here $f$ ... | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 84
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,285 | AMR-119-0081 | Several Complex Variables Problem List — Problem 85 | Prove that if $\Omega$ is strongly pseudoconvex then there is an
absolute constant $K > 0$ such that the integrated Kobayashi distance
between any two points can be realized by a Kobayashi chain of $K$
discs. [For instance, on a convex domain, $K = 1.$] \\
Prize \$50 -S. Krantz. sk @math.wustl.edu | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 85
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,286 | AMR-119-0082 | Several Complex Variables Problem List — Problem 86 | Prove that if $\Omega$ is a smooth bounded pseudoconvex domain in $\mathbb{C}^n$
which is finite type in the sense of D'Angelo, then it is of finite
type in the sense of Kohn (ideal type).\\
Prize \$50 -J. McNeal, mcneal@math.princeton.edu | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 86
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,287 | AMR-120-0001 | Group Actions on 1-Manifolds — Question 1 | Does there exist a lattice in a higher-rank simple Lie group admitting a nontrivial action by orientation-preserving
homeomorphisms of the interval ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 1 (#1)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,288 | AMR-120-0002 | Group Actions on 1-Manifolds — Question 2 | Does there exist an infinite, finitely-generated Kazhdan group of circle homeomorphisms ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 2 (#2)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,289 | AMR-120-0003 | Group Actions on 1-Manifolds — Question 3 | Does there exist a nontrivial (hence infinite) Kazhdan group of orientation-preserving homeomorphisms of the interval ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 3 (#3)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,290 | AMR-120-0004 | Group Actions on 1-Manifolds — Question 4 | Does there exist an infinite, finitely-generated group that acts on the real line all of whose actions
by orientation-preserving homeomorphisms of the line without global fixed points are of type (iii) ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 4 (#4)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,291 | AMR-120-0005 | Group Actions on 1-Manifolds — Question 5 | Does there exist a finitely-generated, amenable, left-orderable group having an isolated order inside an infinite space of left orders ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 5 (#5)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,292 | AMR-120-0006 | Group Actions on 1-Manifolds — Question 6 | Does there exist a finitely-generated, left-orderable group for which the conjugacy action on its space of left orders is minimal
(that is, all the orbits are dense) ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 6 (#6)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,293 | AMR-120-0007 | Group Actions on 1-Manifolds — Question 7 | Does there exist a finitely-generated, left-orderable group without free subgroups and admitting no nontrivial
homomorphism into $\mathbb{Z}$ ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 7 (#7)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,294 | AMR-120-0008 | Group Actions on 1-Manifolds — Question 8 | Does there exist a finitely-generated, left-orderable group $G$ with no nontrivial homomorphism into $\mathbb{Z}$
and trivial group of bounded cohomology $\mathrm{H}^2_b (G, \mathbb{R})$ ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 8 (#8)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,295 | AMR-120-0009 | Group Actions on 1-Manifolds — Question 9 | Is the group of orientation-preserving homeomorphisms of the 2-disk that are the identity at the boundary left orderable ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 9 (#9)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,296 | AMR-120-0010 | Group Actions on 1-Manifolds — Question 11 | Does the group of piecewise-affine circle homeomorphisms contain distorted elements ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 11 (#10)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,297 | AMR-120-0011 | Group Actions on 1-Manifolds — Question 12 | What are the groups of piecewise-projective homeomorphisms of the interval/circle that are
topologically conjugate to groups of $C^1$ diffeomorphisms ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 12 (#11)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,298 | AMR-120-0012 | Group Actions on 1-Manifolds — Question 13 | Given $0 < \alpha < \beta < 1$, does there exist a finitely-generated group of $C^{1+\alpha}$ diffeomorphisms
of the circle/interval that does not embed into the group of $C^{1+\beta}$ diffeomorphisms ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 13 (#12)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,299 | AMR-120-0013 | Group Actions on 1-Manifolds — Question 14 | Let $G$ be a finitely-generated group of $C^2$ circle diffeomorphisms. Assume that $G$ admits an exceptional minimal set
$\Lambda$. Is the Lebesgue measure of $\Lambda$ equal to zero ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 14 (#13)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,300 | AMR-120-0014 | Group Actions on 1-Manifolds — Question 17 | Let $G$ be a finitely-generated group of $C^2$ circle diffeomorphisms. If the action of $G$ is minimal, is it necessarily
ergodic with respect to the Lebesgue measure ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 17 (#16)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
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"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,301 | AMR-120-0015 | Group Actions on 1-Manifolds — Question 18 | Let $G$ be a finitely-generated group of $C^2$ orientation-preserving circle diffeomorphisms. Does there exist a
non-degenerate probability distribution on $G$ for which the stationary measure is absolutely continuous with respect to the Lebesgue measure ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 18 (#17)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,302 | AMR-120-0016 | Group Actions on 1-Manifolds — Question 19 | Given a symmetric, finitely-supported, non-degenerate probability distribution on Thompson's group $T$, does the
Poisson-Furstenberg boundary of $T$ with respect to it identifies with the circle endowed with the corresponding stationary measure ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 19 (#18)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,303 | AMR-120-0017 | Group Actions on 1-Manifolds — Question 20 | Does there exist a faithful action of $\mathbb{Z}^2$ by $C^{\infty}$ orientation-preserving circle diffeomorphisms
that is $C^{\infty}$ structurally stable ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 20 (#19)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,304 | AMR-120-0018 | Group Actions on 1-Manifolds — Question 21 | Given $r \geq 1$, is the subset of $\mathrm{Diff}_+^{r} (\mathrm{S}^1)^2$ consisting of pairs of commuting
diffeomorphisms locally connected ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 21 (#20)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,305 | AMR-120-0019 | Group Actions on 1-Manifolds — Question 22 | Given a faithful action $\phi_0$ of a finitely generated group $G$ by $C^{\infty}$ circle diffeomorphisms
admitting an exceptional minimal set, does there exist a path $\phi_t$ of faithful actions of $G$ that is continuous in the $C^{\infty}$
topology and starts with $\phi_0 = \phi$ so that each $\phi_t$ admits an exce... | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 22 (#21)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,306 | AMR-120-0020 | Group Actions on 1-Manifolds — Question 23 | Let $G$ be a finitely-generated group of circle homeomorphisms whose action is $C^0$ structurally stable.
Suppose that $G$ admits infinitely many non semiconjugate actions on the circle. Does $G$ contain a free subgroup in two generators ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 23 (#22)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,307 | AMR-120-0021 | Group Actions on 1-Manifolds — Question 24 | Let $G$ be a finitely-generated group of $C^1$ circle diffeomorphisms. Suppose that
$G$ has no resilient pairs. Given $\varepsilon > 0$, can $G$ be conjugated (by a homeomorphism) into a group
of Lipschitz homeomorphisms for which the Lipschitz constants of the generators are all $\leq e^{\varepsilon}$ ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 24 (#23)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,308 | AMR-120-0022 | Group Actions on 1-Manifolds — Question 25 | Let $f$ be a $C^2$ circle diffeomorphism of irrational rotation number $\rho$.
Does the set of $C^2$ conjugates of $f$ contain the rotation $R_{\rho}$ in its $C^2$-closure ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 25 (#24)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,309 | AMR-120-0023 | Group Actions on 1-Manifolds — Question 26 | For which values of $r > 1$ there exists $s \geq r$ such that for every $C^s$ circle diffeomorphism $f$ of irrational rotation number $\rho$,
the sequence $f^{q_n}$ converges to the identity in the $C^r$ topology, where $(q_n)$ is the sequence of denominators of the rational approximations of $\rho$ ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 26 (#25)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,310 | AMR-120-0024 | Group Actions on 1-Manifolds — Question 27 | Let $f$ be a $C^2$ circle diffeomorphism of irrational rotation number $\rho$. Given $\varepsilon > 0$, let $M_{\varepsilon}$
be the *mapping torus* of $f$ over $\mathrm{S}^1 \times [0,\varepsilon]$, that is, the surface obtained by identifying $(x,0) \sim (f(x), \varepsilon)$.
Let $\rho (\varepsilon) \in \mathbb{R} / ... | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 27 (#26)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,311 | AMR-120-0025 | Group Actions on 1-Manifolds — Question 28 | Is the (restriction of the) Godbillon-Vey class invariant under topological conjugacy for groups of $C^2$ diffeomorphisms ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 28 (#27)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,312 | AMR-120-0026 | Group Actions on 1-Manifolds — Question 29 | What are the groups of $C^2$ circle diffeomorphisms acting minimally for which the normalizer
inside the group of absolutely continuous homeomorphisms coincides with that inside the group of diffeomorphisms ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 29 (#28)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,313 | AMR-120-0027 | Group Actions on 1-Manifolds — Question 30 | Does Denjoy's theorem hold for circle homeomorphisms whose graphs are real-analytic ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 30 (#29)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,314 | AMR-120-0028 | Group Actions on 1-Manifolds — Question 31 | Is the continuous cohomology of the group $\mathrm{Diff}^{\omega}_+(\mathrm{S}^1)$ of orientation-preserving, real-analytic circle
diffeomorphisms generated by the Euler and the Godbillon--Vey classes ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 31 (#30)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,315 | AMR-120-0029 | Group Actions on 1-Manifolds — Question 32 | Is the group of orientation-preserving $C^2$ circle diffeomorphisms simple ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 32 (#31)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,316 | AMR-120-0030 | Group Actions on 1-Manifolds — Question 33 | Does the Tits alternative hold in $\mathrm{Diff}_+^{\omega} (\mathrm{S}^1)$ ? More precisely,
does every non-metabelian subgroup of this group contain a free subgroup ? | Source list: Navas - Group Actions on 1-Manifolds: A List of Very Concrete Open Questions (2017)
Source item: Question 33 (#32)
Source URL: https://arxiv.org/abs/1712.06462
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Navas | 2,017 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,317 | AMR-121-0001 | Complexity in Enumerative Combinatorics — Conjecture 1 (Wilf) | Now, for a *combinatorial sequence* $\{a_n\}$ one can ask if there is a
Wilfian formula. In the original paper [Wilf] an explicit example is given:
Let $a_n$ be the number of unlabeled graphs on $n$ vertices. Then $\{a_n\}$ has
no Wilfian formula of type \textup{\small $($\textrm{W1}$)$}. | Source list: Pak - Complexity Problems in Enumerative Combinatorics (2018)
Source item: Conjecture 1
Source URL: https://arxiv.org/abs/1803.06636
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Wilf | 3 | open | Pak | 2,018 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,318 | AMR-121-0002 | Complexity in Enumerative Combinatorics — Conjecture 2 | Let $a_n$ be the number of unlabeled plane
triangulations with $n$ vertices, and let $b_n$ be the number of
$3$-connected planar graphs with $n$ vertices.
Then $\{a_n\}$ and $\{b_n\}$ can be computed
in \mathrm{poly}$(n)$ time. | Source list: Pak - Complexity Problems in Enumerative Combinatorics (2018)
Source item: Conjecture 2
Source URL: https://arxiv.org/abs/1803.06636
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Pak | 2,018 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,319 | AMR-121-0003 | Complexity in Enumerative Combinatorics — Conjecture 3 | It was shown in [Ges] that similar polynomial recurrences exist for the number
of $k$-regular labeled graphs, for every fixed $k\ge 1$.
Fix $k\ge 1$ and let $a_n$ be the number of unlabeled
$k$-regular graphs with $n$ vertices. Then $\{a_n\}$
can be computed in \textup{\textrm{poly}}$(n)$ time. | Source list: Pak - Complexity Problems in Enumerative Combinatorics (2018)
Source item: Conjecture 3
Source URL: https://arxiv.org/abs/1803.06636
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Pak | 2,018 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,320 | AMR-121-0004 | Complexity in Enumerative Combinatorics — Conjecture 4 | For a fixed ${\text **T** } $, let $g(m,n)$ denote the number of tilings of
$[m\times n]$ with ${\text **T** } $. Is $g(m,n)$ computable in polynomial
time? The following conjecture suggests otherwise.
There exists a finite set of tiles ${\text **T** } $ such that counting
the number of tilings of
$[n\times n]$ } $ is... | Source list: Pak - Complexity Problems in Enumerative Combinatorics (2018)
Source item: Conjecture 4
Source URL: https://arxiv.org/abs/1803.06636
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Pak | 2,018 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,321 | AMR-121-0005 | Complexity in Enumerative Combinatorics — Problem 5 (Pak--Yeliussizov) | This also implies that $y(t)$ is not D-finite. Indeed, observe by definition,
that if a sequence $\{a_n\}$ is P-recursive, then so is $\{n! $,
which implies the result by taking $a_n=B_n/n!$ (cf. [LR]). Of course,
there is a more direct way to prove that $y(t)$ is not $D$-finite by
repeated differentiation or via the a... | Source list: Pak - Complexity Problems in Enumerative Combinatorics (2018)
Source item: Problem 5
Source URL: https://arxiv.org/abs/1803.06636
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Pak--Yeliussizov | 3 | open | Pak | 2,018 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,322 | AMR-121-0006 | Complexity in Enumerative Combinatorics — Conjecture 6 | Before we proceed to more combinatorial examples, let us mention that
D-transcendental GFs are the subject of *Differential Galois Theory*,
which goes back to Liouville, Lie, Picard and Vessiot in the 19th century
(see e.g. [Ritt]), and continues to be developed [Put-S]. Some
natural GFs are known to be D-transcendenta... | Source list: Pak - Complexity Problems in Enumerative Combinatorics (2018)
Source item: Conjecture 6
Source URL: https://arxiv.org/abs/1803.06636
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Pak | 2,018 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,323 | AMR-121-0007 | Complexity in Enumerative Combinatorics — Conjecture 7 | Here $p_n$ is the $n$-th prime, and $\pi(n)$ is the number of primes $\le n$,
as above. Both GFs are known to be non-D-finite, as shown by
Flajolet, Gerhold and Salvy in [FGS] by asymptotic
arguments. The authors quip: ``*Almost anything
is non-holonomic unless it is holonomic by design*''.
Well, maybe so. But the same... | Source list: Pak - Complexity Problems in Enumerative Combinatorics (2018)
Source item: Conjecture 7
Source URL: https://arxiv.org/abs/1803.06636
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Pak | 2,018 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,324 | AMR-121-0008 | Complexity in Enumerative Combinatorics — Conjecture 8 (cf. [Zei]) | Let $a_n$ denotes the number of self-avoiding walks $O\to O$
in $\mathbb{Z}^2$ of length $n$. Then the sequence $\{a_n\}$ has
no Wilfian formula of type \textup{\small $($\textrm{W1}$)$}. | Source list: Pak - Complexity Problems in Enumerative Combinatorics (2018)
Source item: Conjecture 8
Source URL: https://arxiv.org/abs/1803.06636
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: cf. [Zei] | 3 | open | Pak | 2,018 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,325 | AMR-121-0009 | Complexity in Enumerative Combinatorics — Problem 9 | In a forthcoming paper [GP-ADE]
we construct an explicit but highly artificial non-symmetric set
$S\subset F_k\times F_\ell$
In [KP2] we use the tools in [KP1] to prove that
groups have an uncountable set of *spectral radii*
$$
\rho(G,S) := \lim_{n\to \infty} a_n(G,S)^{1/n}
$$
Since the set of D-algebraic sequence is c... | Source list: Pak - Complexity Problems in Enumerative Combinatorics (2018)
Source item: Problem 9
Source URL: https://arxiv.org/abs/1803.06636
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Pak | 2,018 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,326 | AMR-121-0010 | Complexity in Enumerative Combinatorics — Problem 10 | Can }}_n(1324)\}$ $(n)$
time? (In 2005, Doron Zeilberger expressed doubts that
$\text{{\rm \textsf{A}}}_{1000}(1324)$
This sentiment has been roundly criticized on both mathematical
and theological grounds (see [Ste]). ) More generally,
can one find a single permutation $\pi$ such that
}}_n(\pi)\}$ $(n)$
time? Is the c... | Source list: Pak - Complexity Problems in Enumerative Combinatorics (2018)
Source item: Problem 10
Source URL: https://arxiv.org/abs/1803.06636
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Pak | 2,018 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,327 | AMR-121-0011 | Complexity in Enumerative Combinatorics — Problem 11 | One especially notable case of a combinatorial interpretation
is the problem of computing the
*Kronecker coefficients* of the symmetric group, which are defined by
$$\chi^\lambda \cdot \chi^\mu = \sum_{\nu\vdash n}
g(\lambda,\mu,\nu) \. \chi^\nu, \quad \text{where} \ \ \lambda,\mu \vdash n
$$
and $\chi^\lambda,
of $S_n... | Source list: Pak - Complexity Problems in Enumerative Combinatorics (2018)
Source item: Problem 11
Source URL: https://arxiv.org/abs/1803.06636
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Pak | 2,018 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,328 | AMR-121-0012 | Complexity in Enumerative Combinatorics — Problem 12 | The original proof is an elegant double counting argument modulo $2$.
This suggests the following open problem: (This problem
was suggested to us by Peter Shor
https://tinyurl.com/y7yafneh (https://cstheory.stackexchange.com/questions/33508).)
Find a combinatorial interpretation for $N_e(G)/2$. | Source list: Pak - Complexity Problems in Enumerative Combinatorics (2018)
Source item: Problem 12
Source URL: https://arxiv.org/abs/1803.06636
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Pak | 2,018 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,329 | AMR-121-0013 | Complexity in Enumerative Combinatorics — Conjecture 13 (cf. [Ges-sem]) | In [Ges-sem], the author defined the following *Gessel sequence*:
$$
b_n := \ 2\cdot 5^n \. - \. (3+4i)^{n} \. - \. (3-4i)^{n}, \quad \text{where} \ \ i \. = \. \sqrt{-1}
$$
see also [OEIS, A250102 (https://oeis.org/A250102)].
Note that $b_n\in \mathbb{Z}$ since
$$b_n = 2\cdot 5^n \. - \. 2 {2r} \. 3^{n-2r}
$$
and that... | Source list: Pak - Complexity Problems in Enumerative Combinatorics (2018)
Source item: Conjecture 13
Source URL: https://arxiv.org/abs/1803.06636
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: cf. [Ges-sem] | 3 | open | Pak | 2,018 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,330 | AMR-122-0001 | Enumeration of Matchings — Problem 1 | Show that in the $2n-1,2n,2n-1$ semiregular hexagon,
the central location (consisting of the two innermost triangles) is
covered by a lozenge in exactly one-third of the tilings.
(Equivalently: Show that if one chooses a random perfect matching of
the dual graph, the probability that the central edge is contained
in t... | Source list: Propp - Twenty Open Problems in Enumeration of Matchings (1998)
Source item: Problem 1 (#1)
Source URL: https://arxiv.org/abs/math/9801060
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 1,998 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,331 | AMR-122-0002 | Enumeration of Matchings — Problem 2 | \end{verbatim}
These are similar to the numbers one gets from counting lozenge-tilings
of an $n,n,n,n,n,n$ hexagon, in that the largest prime factor seems to
be bounded by a linear function of $n$, and it ought to be possible to
come up with a conjectural exact formula. What might be harder is
proving it.
Enumerate th... | Source list: Propp - Twenty Open Problems in Enumeration of Matchings (1998)
Source item: Problem 2 (#2)
Source URL: https://arxiv.org/abs/math/9801060
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 1,998 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,332 | AMR-122-0003 | Enumeration of Matchings — Problem 3 | 10 3 8 2 4 2
(2) (3) (5) (13) (17) (19)
2 2 2 3 4 4 8 4
(2) (5) (7) (11) (13) (17) (19) (23)
\end{verbatim}
Enumerate the lozenge-tilings of the region obtained
from the $2n,2n+3,2n,2n+3,2n,2n+3$ hexagon by removing a triangle from
the middle of each of its long sides. | Source list: Propp - Twenty Open Problems in Enumeration of Matchings (1998)
Source item: Problem 3 (#3)
Source URL: https://arxiv.org/abs/math/9801060
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 1,998 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,333 | AMR-122-0004 | Enumeration of Matchings — Problem 4 | Determine the number of lozenge-tilings of a
regular hexagon from which two of its innermost unit triangles
(one upward-pointing and one downward-pointing) have been removed. | Source list: Propp - Twenty Open Problems in Enumeration of Matchings (1998)
Source item: Problem 4 (#4)
Source URL: https://arxiv.org/abs/math/9801060
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 1,998 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,334 | AMR-122-0005 | Enumeration of Matchings — Problem 5 | Determine the cokernel of the Carlitz matrices,
or equivalently of the Kasteleyn matrices of $a,b,c$ hexagons, and
if possible find a way to interpret the cokernel in terms of
the tilings.
He points out that in the case $a=b=c=2$, one gets a non-cyclic group
as the cokernel. | Source list: Propp - Twenty Open Problems in Enumeration of Matchings (1998)
Source item: Problem 5 (#5)
Source URL: https://arxiv.org/abs/math/9801060
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 1,998 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,335 | AMR-122-0006 | Enumeration of Matchings — Problem 6 | Digressing for a moment from the topic of lozenge tilings,
I point out that
in general, the Kasteleyn matrix $K$ is not canonically defined,
in the sense that there may be many ways of modifying the
signs of certain entries of the bipartite adjacency matrix
of a graph so that all non-zero contributions to the
determina... | Source list: Propp - Twenty Open Problems in Enumeration of Matchings (1998)
Source item: Problem 6 (#6)
Source URL: https://arxiv.org/abs/math/9801060
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 1,998 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,336 | AMR-122-0007 | Enumeration of Matchings — Problem 7 | Find the ``vertical moments of inertia'' for the mass on
edges arising from edge-probabilities for random matchings of the
$a,b,c$ honeycomb graph. | Source list: Propp - Twenty Open Problems in Enumeration of Matchings (1998)
Source item: Problem 7 (#7)
Source URL: https://arxiv.org/abs/math/9801060
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 1,998 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,337 | AMR-122-0008 | Enumeration of Matchings — Problem 8 | 47 2
(2) (3) (5)
\end{verbatim}
Note that only the presence of the large prime factor 73 makes one doubt
that there is a general formula; the other prime factors are reassuringly
small. Further data might make it clear what that 73 is doing there.
Count the domino tilings of an Aztec diamond from which
two close-to-ce... | Source list: Propp - Twenty Open Problems in Enumeration of Matchings (1998)
Source item: Problem 8 (#8)
Source URL: https://arxiv.org/abs/math/9801060
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 1,998 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,338 | AMR-122-0009 | Enumeration of Matchings — Problem 9 | One can also look at ``Aztec rectangles'' from which squares have been
removed so as to restore the balance between black and white squares
(a necessary condition for tilability). For instance, one can remove
the central square from an $a$-by-$b$ Aztec rectangle in which $a$
and $b$ differ by 1, with the larger of $a,b... | Source list: Propp - Twenty Open Problems in Enumeration of Matchings (1998)
Source item: Problem 9 (#9)
Source URL: https://arxiv.org/abs/math/9801060
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 1,998 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,339 | AMR-122-0010 | Enumeration of Matchings — Problem 10 | What about $(2n-1)$-by-$2n$ rectangles? For these regions, removing
the central square does not make the region tilable. However, if
one removes any one of the four squares adjacent to the middle square,
one obtains a region that is tilable, and moreover, for this region
the number of tilings appears to be a nice round... | Source list: Propp - Twenty Open Problems in Enumeration of Matchings (1998)
Source item: Problem 10 (#10)
Source URL: https://arxiv.org/abs/math/9801060
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 1,998 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,340 | AMR-122-0011 | Enumeration of Matchings — Problem 11 | Perhaps this is a special case of a two-parameter fact that says that
you can take an intrusion of length $m$ in a $2n$-by-$2n$ square and the
number of tilings of the resulting region will always be a square or
twice a square.
What is going on with ``intruded Aztec diamonds''?
In particular, why is the number of tili... | Source list: Propp - Twenty Open Problems in Enumeration of Matchings (1998)
Source item: Problem 11 (#11)
Source URL: https://arxiv.org/abs/math/9801060
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 1,998 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,341 | AMR-122-0012 | Enumeration of Matchings — Problem 12 | Consider the Kasteleyn matrix $K_n$ for the Aztec diamond of order $n$,
in which every other vertical domino has its sign flipped (that is,
the corresponding 1's in the bipartite adjacency matrix are
replaced by $-1$'s).
Show that the sum of the entries of the matrix inverse
of $K_n$ is $(n-1)(n+3)/2 - 2^{n-1} + 2$.
... | Source list: Propp - Twenty Open Problems in Enumeration of Matchings (1998)
Source item: Problem 12 (#12)
Source URL: https://arxiv.org/abs/math/9801060
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 1,998 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,342 | AMR-122-0013 | Enumeration of Matchings — Problem 13 | Find a general formula for the number of domino tilings
of even pillows. | Source list: Propp - Twenty Open Problems in Enumeration of Matchings (1998)
Source item: Problem 13 (#13)
Source URL: https://arxiv.org/abs/math/9801060
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 1,998 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,343 | AMR-122-0014 | Enumeration of Matchings — Problem 14 | Find a general formula for the number of domino tilings
of Aztec windows.
Even an argument explaining why the number of tilings for windows
of inner order $x$ and outer order $x+w$ should be given by a polynomial
in $x$ (for each fixed $w$) would constitute progress! | Source list: Propp - Twenty Open Problems in Enumeration of Matchings (1998)
Source item: Problem 14 (#14)
Source URL: https://arxiv.org/abs/math/9801060
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 1,998 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,344 | AMR-122-0015 | Enumeration of Matchings — Problem 15 | One case that has not yet been settled
is the case that arises from a rather symmetric
dissection of the plane into
equilateral triangles, squares, and regular hexagons,
with 4 polygons meeting at each vertex.
Empirically, one finds that
the number of diform tilings is
$2^{n(n+1)}$.
Prove that for the Aztec-type regio... | Source list: Propp - Twenty Open Problems in Enumeration of Matchings (1998)
Source item: Problem 15 (#15)
Source URL: https://arxiv.org/abs/math/9801060
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 1,998 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,345 | AMR-122-0016 | Enumeration of Matchings — Problem 16 | For instance, we have the roughly hexagonal region shown at the top of
the next page
(a union of square and triangular pieces, with certain boundary vertices
marked with a ``.''\ so as to bring out the large-scale 2,3,2,2,3,2 hexagonal
structure more clearly);
it has 17920 tilings, where 17920 is $2^9 \cdot 5 \cdot 7$.... | Source list: Propp - Twenty Open Problems in Enumeration of Matchings (1998)
Source item: Problem 16 (#16)
Source URL: https://arxiv.org/abs/math/9801060
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 1,998 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
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"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
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"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,346 | AMR-122-0017 | Enumeration of Matchings — Problem 17 | Characterize those local substitutions that have
a predictable effect on the weighted sum of matchings of a graph.
The most useful local substitution so far has been
\begin{verbatim}
q q
| C / \ D
a u b / \
/ \ / \
p---t v---r ----> p r
\ / \ /
d w c \ /
| B \ / A
s s
\end{verbatim}
(where unmarked edges have weight ... | Source list: Propp - Twenty Open Problems in Enumeration of Matchings (1998)
Source item: Problem 17 (#17)
Source URL: https://arxiv.org/abs/math/9801060
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 1,998 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,347 | AMR-122-0018 | Enumeration of Matchings — Problem 18 | How many perfect matchings does the triangle graph
of order $n$ have? | Source list: Propp - Twenty Open Problems in Enumeration of Matchings (1998)
Source item: Problem 18 (#18)
Source URL: https://arxiv.org/abs/math/9801060
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 1,998 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,348 | AMR-122-0019 | Enumeration of Matchings — Problem 19 | One can also look at graphs that are bipartite but not planar.
A natural example is the $n$-cube (that is, the $n$-dimensional cube
with all sides of length 2). It has been shown that the number
of perfect matchings of the $n$-cube goes like $1$, $2$, $9=3^2$,
$272=16 \cdot 17$,
$589185=3^2 \cdot 5 \cdot 13093$, $\dots... | Source list: Propp - Twenty Open Problems in Enumeration of Matchings (1998)
Source item: Problem 19 (#19)
Source URL: https://arxiv.org/abs/math/9801060
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 1,998 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,349 | AMR-123-0001 | Trimer Covers in the Triangular Grid — Problem 1 | Find an exact formula for $T_{003}(k(3k-1)/2,k(3k+1)/2)$.
Of course, even short of an exact formula,
any method of determining the number of tilings
that is more efficient than brute-force enumeration
(e.g., a recurrence relation) would be of interest.
See [KiPr] for more discussion of no-stones tilings of benzels. | Source list: Propp - Trimer Covers in the Triangular Grid: Twenty Mostly Open Problems (2022)
Source item: Problem 1 (#1)
Source URL: https://arxiv.org/abs/2206.06472
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 2,022 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,350 | AMR-123-0002 | Trimer Covers in the Triangular Grid — Problem 4 | When $a$ and $b$ are such that
the Conway-Lagarias invariant is strictly positive,
the $(a,b)$-benzel cannot be tiled by bones and left stones;
the corresponding entries in the table must be zero.
On the other hand, when $a$ and $b$ are such that
the Conway-Lagarias invariant is negative or zero,
the entries in the tab... | Source list: Propp - Trimer Covers in the Triangular Grid: Twenty Mostly Open Problems (2022)
Source item: Problem 4 (#2)
Source URL: https://arxiv.org/abs/2206.06472
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 2,022 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,351 | AMR-123-0003 | Trimer Covers in the Triangular Grid — Problem 7 | In parallel with the observations that preceded Problem 4,
note that when the Conway-Lagarias invariant of a benzel is strictly negative,
the benzel cannot be tiled by bones and right-pointing stones;
the corresponding entries in the table must be zero.
On the other hand, when $a$ and $b$ are such that
the Conway-Lagar... | Source list: Propp - Trimer Covers in the Triangular Grid: Twenty Mostly Open Problems (2022)
Source item: Problem 7 (#3)
Source URL: https://arxiv.org/abs/2206.06472
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 2,022 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,352 | AMR-123-0004 | Trimer Covers in the Triangular Grid — Problem 11 | With $T(n) = T_{112}(3n-1,3n)$ with $n \geq 1$,
it appears that $T(n)$ has no prime factor greater than or equal to $4n$.
Find a formula governing $T_{112}(3n-1,3n)$. See
OEIS entry A364483 (https://oeis.org/A364483).
We now switch from central diagonals to peripheral diagonals. | Source list: Propp - Trimer Covers in the Triangular Grid: Twenty Mostly Open Problems (2022)
Source item: Problem 11 (#4)
Source URL: https://arxiv.org/abs/2206.06472
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 2,022 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,353 | AMR-123-0005 | Trimer Covers in the Triangular Grid — Problem 12 | Is it true that $T_{112}(n+2,2n+1)$
is the ``$n$th large Schr\"oder number''
(see OEIS entry A006318 (https://oeis.org/A006318))
for all $n \geq 1$?
Equality has been verified for $1 \leq n \leq 15$. | Source list: Propp - Trimer Covers in the Triangular Grid: Twenty Mostly Open Problems (2022)
Source item: Problem 12 (#5)
Source URL: https://arxiv.org/abs/2206.06472
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 2,022 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,354 | AMR-123-0006 | Trimer Covers in the Triangular Grid — Problem 13 | Is it true that $T_{112}(n+2,2n)$
is the number of ``royal paths in a lattice of order $n$''
(see OEIS entry A006319 (https://oeis.org/A006319))
for all $n \geq 1$?
Equality has been verified for $1 \leq n \leq 15$. | Source list: Propp - Trimer Covers in the Triangular Grid: Twenty Mostly Open Problems (2022)
Source item: Problem 13 (#6)
Source URL: https://arxiv.org/abs/2206.06472
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 2,022 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,355 | AMR-123-0007 | Trimer Covers in the Triangular Grid — Problem 15 | Is $T_{113}(n,2n-4)$
2-adically continuous as a function of $n \geq 5$?
Comment: The sequence appears to be constant mod 2, constant mod 4,
2-periodic mod 8, and 8-periodic mod 16
(with repeating pattern 4, 4, 4, 4, 4, 12, 4, 12).
The case $n = 4$ breaks the pattern.
See OEIS entry A364416 (https://oeis.org/A364416). | Source list: Propp - Trimer Covers in the Triangular Grid: Twenty Mostly Open Problems (2022)
Source item: Problem 15 (#7)
Source URL: https://arxiv.org/abs/2206.06472
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 2,022 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,356 | AMR-123-0008 | Trimer Covers in the Triangular Grid — Problem 16 | Is $T_{113}(n,2n-3)$
2-adically continuous as a function of $n \geq 4$?
Comment: The sequence appears to be constant mod 2, constant mod 4,
2-periodic mod 8, and 8-periodic mod 16
(with repeating pattern 2, 14, 2, 14, 10, 6, 10, 6).
The case $n = 3$ breaks the pattern.
See OEIS entry A364417 (https://oeis.org/A364417)... | Source list: Propp - Trimer Covers in the Triangular Grid: Twenty Mostly Open Problems (2022)
Source item: Problem 16 (#8)
Source URL: https://arxiv.org/abs/2206.06472
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 2,022 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,357 | AMR-123-0009 | Trimer Covers in the Triangular Grid — Problem 17 | Is $T_{113}(n,2n-4;3)$
2-adically continuous as a function of $n \geq 5$?
Comment: The sequence appears to be constant mod 2, constant mod 4,
constant mod 8, and 8-periodic mod 16
(with repeating pattern 4, 4, 12, 12, 4, 12, 12, 4).
The case $n = 4$ breaks the pattern.
See OEIS entry A364418 (https://oeis.org/A364418)... | Source list: Propp - Trimer Covers in the Triangular Grid: Twenty Mostly Open Problems (2022)
Source item: Problem 17 (#9)
Source URL: https://arxiv.org/abs/2206.06472
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 2,022 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,358 | AMR-123-0010 | Trimer Covers in the Triangular Grid — Problem 18 | Comment: The sequence appears to be constant mod 2, constant mod 4,
constant mod 8, and 8-periodic mod 16
(with repeating pattern 4, 4, 12, 12, 4, 12, 12, 4).
The case $n = 4$ breaks the pattern.
See OEIS entry A364418 (https://oeis.org/A364418).
Is $T_{113}(n,2n-3;3)$
2-adically continuous as a function of $n \geq 4$... | Source list: Propp - Trimer Covers in the Triangular Grid: Twenty Mostly Open Problems (2022)
Source item: Problem 18 (#10)
Source URL: https://arxiv.org/abs/2206.06472
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 2,022 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,359 | AMR-123-0011 | Trimer Covers in the Triangular Grid — Problem 20 | The question we ask is, how many such tiling are there?
OEIS entry A334875 (https://oeis.org/A334875)
gives the answers for small values of $n$.
If we look at the prime factorizations of the answers,
we notice that the exponent of the prime 2 is creeping upward.
Specifically, the multiplicity of the prime 2
in the fact... | Source list: Propp - Trimer Covers in the Triangular Grid: Twenty Mostly Open Problems (2022)
Source item: Problem 20 (#11)
Source URL: https://arxiv.org/abs/2206.06472
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Propp | 2,022 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,360 | AMR-124-0001 | Iwahori-Hecke Algebras — Problem 1 | Let $I$ be a finite set and let $(m_{ij})_{(i,j)\in I\times I}$ be a symmetric matrix whose diagonal entries are $1$
and whose nondiagonal entries are integers $\ge2$ or $\infty$. Let $W$ be the group with generators
$\{s_i;i\in I\}$ and relations $(s_is_j)^{m_{ij}}=1$ for any $i,j$ such that $m_{ij}<\infty$; this is a... | Source list: Lusztig - Open Problems on Iwahori-Hecke Algebras (2020)
Source item: Problem 1
Source URL: https://arxiv.org/abs/2006.08535
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Lusztig | 2,020 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,361 | AMR-124-0002 | Iwahori-Hecke Algebras — Problem 2 | There is a unique group homomorphism $\bar{}:H@>>>H$ such that $\overline{v^nT_w}T_{w\i}=v^{-n}$ for
$n\in\mathbb{Z},w\in W$; it is a ring isomorphism. Let $H_{\le0}=\sum_{w\in W}\mathbb{Z}[v
- ]T_w\subset H$.
For any $w\in W$ there is a unique element $c_w\in H_{\le0}$ such that $\bar c_w=c_w$ and
$c_w-T_w\in v
- H_{\... | Source list: Lusztig - Open Problems on Iwahori-Hecke Algebras (2020)
Source item: Problem 2
Source URL: https://arxiv.org/abs/2006.08535
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Lusztig | 2,020 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,362 | AMR-124-0003 | Iwahori-Hecke Algebras — Problem 3 | Assume that $W$ is finite and that $L=||$. Let $C$ be a conjugacy class in $W$; let
$C_{min}$ be the set of all $w\in C$ such that $|w|$ is minimal. For $w\in C$ let $N^w\in A$
be the trace of the
$A$-linear map $H@>>>H$, $h\mapsto v^{2|w|}T_whT_{w\i}$. We have $N^w\in\mathbb{Z}[v^2]$. (Note that $N^w|_{v=1}$ is the
or... | Source list: Lusztig - Open Problems on Iwahori-Hecke Algebras (2020)
Source item: Problem 3
Source URL: https://arxiv.org/abs/2006.08535
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Lusztig | 2,020 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,363 | AMR-125-0001 | Coxeter Groups and Unimodality — Problem 1 | It is well known (see, e.g., [Hum, Prop. 5.12] or [BB, Cor. 7.1.4])
that if $(W,S)$ is a Coxeter system then $\sum_{u \in W} x^{\ell(u)}$ is a rational generating function.
The following problem was proposed by Stembridge in [Ste97].
Let $(W,S)$ be a Coxeter system. Is it true that then
\[
\sum_{t \in T} x^{\ell(t)}
\... | Source list: Brenti - Some Open Problems on Coxeter Groups and Unimodality (2024)
Source item: Problem 1
Source URL: https://arxiv.org/abs/2410.09897
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Brenti | 2,024 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,364 | AMR-125-0002 | Coxeter Groups and Unimodality — Conjecture 2 | Let $(W_1,S_1)$, $(W_2,S_2)$ be two Coxeter systems, and $u,v \in W_1$, $w,z \in W_2$ be such that $[u,v] \simeq [w,z]$ (isomorphic as posets). Then
\begin{equation}
P_{u,v}(q)=P_{w,z}(q).
\end{equation} | Source list: Brenti - Some Open Problems on Coxeter Groups and Unimodality (2024)
Source item: Conjecture 2
Source URL: https://arxiv.org/abs/2410.09897
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Brenti | 2,024 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,365 | AMR-125-0003 | Coxeter Groups and Unimodality — Conjecture 3 | Let $(W_1,S_1)$, $(W_2,S_2)$ be two Coxeter systems, $J_1 \subseteq S_1$, $J_2 \subseteq S_2$, $u,v \in W_1^{J_1}$, $w,z \in W_2^{J_2}$ and $f: [u,v] \rightarrow [w,z]$ be a poset isomorphism such that $f([u,v]^{J_1})=[w,z]^{J_2}$. Then
\begin{equation}
P_{u,v}^{J_1,q}(q)=P_{w,z}^{J_2,q}(q).
\end{equation} | Source list: Brenti - Some Open Problems on Coxeter Groups and Unimodality (2024)
Source item: Conjecture 3
Source URL: https://arxiv.org/abs/2410.09897
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Brenti | 2,024 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,366 | AMR-125-0004 | Coxeter Groups and Unimodality — Conjecture 4 | Let $W$ be a Weyl group of type $A$ and $u,v \in W$, $u \leq v$. Then
\begin{equation}
P_{u,v}(q) = \widetilde{P}_{u,v,z}(q)
\end{equation}
for any hypercube decomposition $[u,z]$ of $[u,v]$. | Source list: Brenti - Some Open Problems on Coxeter Groups and Unimodality (2024)
Source item: Conjecture 4
Source URL: https://arxiv.org/abs/2410.09897
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Brenti | 2,024 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,367 | AMR-125-0005 | Coxeter Groups and Unimodality — Conjecture 5 | Let $(W,S)$ be a Coxeter system, and $u,v \in W$, $u \leq v$. Then
\[
\widetilde{\Phi}_{u,v} \in \mathbb{N} \langle c,d \rangle.
\] | Source list: Brenti - Some Open Problems on Coxeter Groups and Unimodality (2024)
Source item: Conjecture 5
Source URL: https://arxiv.org/abs/2410.09897
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Brenti | 2,024 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,368 | AMR-125-0006 | Coxeter Groups and Unimodality — Problem 6 | It is known ([Polo], see also [CasRep]) that if $P(q) \in \mathbb{N}[q]$ is such that $P(0)=1$ then there are $n \in \mathbb{P}$ and $u,v \in S_n$ such that $P(q)=P_{u,v}(q)$. The following related problem was posed by Bj\"{o}rner ([BjoPC]).
Let $(W,S)$ be a Coxeter system and $u,v \in W$, $u \leq v$. Is it true that
... | Source list: Brenti - Some Open Problems on Coxeter Groups and Unimodality (2024)
Source item: Problem 6
Source URL: https://arxiv.org/abs/2410.09897
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Brenti | 2,024 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,369 | AMR-125-0007 | Coxeter Groups and Unimodality — Problem 7 | The proof of the celebrated nonnegativity conjecture for Kazhdan-Lusztig polynomials
([EW]) makes the following problem even more compelling.
Find a combinatorial interpretation for Kazhdan-Lusztig polynomials. | Source list: Brenti - Some Open Problems on Coxeter Groups and Unimodality (2024)
Source item: Problem 7
Source URL: https://arxiv.org/abs/2410.09897
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Brenti | 2,024 | 2 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
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