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README.md

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 ---
-license: cc-by-2.0
+tags:
+- permutation
+- algorithmic-reasoning
+- synthetic
+- sequence-classification
+task_categories:
+- sequence-modeling
+pretty_name: Permutation Same-Cycle Matrices
+size_categories:
+- 10K<n<100K
 ---
+
+# Permutation same-cycle matrices
+
+Synthetic data for predicting whether two individuals belong to the same cycle of a permutation. Each example contains a zero-based permutation and its binary cycle-equivalence matrix. Entry `(i, j)` is `1` exactly when individuals `i` and `j` are in the same cycle.
+
+## Contents
+
+The dataset includes permutation sizes `p = 7, 8, 9, 10`. For each size there are 4,096 training examples and 100 test examples. Within each size, train and test permutations are sampled uniformly without replacement and are disjoint. The sampling seed is `0`.
+
+Files are split by permutation size so the matrix shape is explicit: `data/p7-train-00000-of-00001.parquet`, through `p10-test-00000-of-00001.parquet`.
+
+## Features
+
+- `permutation`: zero-based permutation tokens, length `p`
+- `same_cycle`: binary `p x p` matrix
+- `permutation_size`: `p`
+- `source_rank`: lexicographic rank of the sampled permutation
+
+## Load
+
+```python
+from datasets import load_dataset
+
+train_files = [
+    "data/p7-train-00000-of-00001.parquet",
+    "data/p8-train-00000-of-00001.parquet",
+    "data/p9-train-00000-of-00001.parquet",
+    "data/p10-train-00000-of-00001.parquet",
+]
+test_files = [f.replace("-train-", "-test-") for f in train_files]
+ds = load_dataset("parquet", data_files={"train": train_files, "test": test_files})
+```
+
+The data-generation logic is based on `predict_integers_in_same_cycle/data_generation.py`.

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