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README.md

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-license: cc-by-2.0
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+license: cc-by-2.0
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+# Dataset Card for Characters of Irreducible Representations of the Symmetric Group, \\(S_n\\), n = 22
+
+Weaving patterns are \\(n \times n−1\\)-matrices with \\(\{1, 2, . . . , n\}\\)-
+entries introduced by \[1\] to study the number of reduced decompositions of the 
+permutation \\(\sigma = n\; n − 1 \;\dots\; 1\\) up to commutation equivalence. The number
+of such objects also counts the number of parallel sorting
+networks, the number of rhombic tilings of regular polygons, and is connected to 
+the study of the higher Bruhat orders \[2\]. An \\(O(n^2)\\) algorithm for determining
+if a given \\(\{1, 2, . . . , n\}\\)-matrix is a valid weaving pattern
+exists but gives no additional insight into the structure of
+weaving patterns and correspondingly the asymptotics of
+reduced decompositions. The enumeration of reduced decompositions 
+up to commutation equivalence has been studied by many including
+Knuth and Stanley. An exact formula is likely out of reach,
+so asymptotic upper and lower bounds are of great interest.
+ML models that can detect necessary or sufficient conditions
+for a matrix to be a valid weaving pattern have the potential
+to lead to substantial improvements in the upper bound.
+
+Each dataset is a mixture of enriched weaving patterns and
+non-weaving pattern matrices with \\(\{1, 2, . . . , n\}\\)-entries.
+
+## Dataset Details
+
+Weaving patterns of size \\(n \times n − 1\\) are a special type of matrix containing 
+entries in \\(\{1, 2, . . . , n\}\\). They correspond to representations of the 
+longest word permutation of \\(n\\) elements (the permutation that sends 
+\\(1 \mapsto n\\), \\(2 \mapsto n − 1\\), etc.). This
+task involves trying to identify weaving patterns among matrices that look like weaving patterns but are not.
+Each matrix is stored on a single line in row-major format. For instance,
+
+`(0, 1, 2, 3, 3, 2, 3, 4, 2, 3, 2, 1, 5, 4, 3, 2)`
+
+The datasets can also be found [here](https://drive.google.com/file/d/15AHAn9NnC7crzG_8BnaH3pp1aOGUUniV/view?usp=sharing).
+Data loaders can be found [here](https://github.com/pnnl/ML4AlgComb/tree/master/weaving_patterns).
+
+**Statistics**
+|  | Weaving patterns | Non-weaving patterns |
+|----------|----------|---------------|
+| Train | 634 | 1,116 |
+| Test  | 275 | 467 |
+
+This dataset is small, we encourage users to also look at the dataset for \\(n = 7\\).
+
+**Math question:** Find an algorithm or set of rules that can efficiently distinguish between 
+weaving pattern matrices and non-weaving pattern matrices. This should be more efficient than the 
+\\(O(n^2\\) algorithm that can be found in the references above.
+
+**ML task:** Train a model to classify whether a \\({1, 2, . . . , n\}\\)-
+matrix is a weaving pattern or not. This task is framed as
+binary classification. Extract mathematical insights from a performant model.
+
+If a successful model is trained, it would be interesting to understand whether the model has 
+learned an existing algorithm or whether it has discovered something new.
+
+## Small model performance
+
+We provide some basic baselines for this task. Benchmarking details can be found in the associated paper.
+
+| Size | Logistic regression | MLP | Transformer | Guessing training label mean | 
+|----------|----------|-----------|------------|------------|
+| \\(n= 6\\) | \\(70.4\%\\) | \\(86.1 \% \pm 0.2\%\\) | \\(85.9\% \pm 2.3\%\\)| \\(63.3\%\\) |
+
+The \\(\pm\\) signs indicate 95% confidence intervals from random weight initialization and training.
+
+- **Curated by:** Herman Chau
+- **Funded by:** Pacific Northwest National Laboratory
+- **Language(s) (NLP):** NA
+- **License:** CC-by-2.0
+
+### Dataset Sources
+
+Data generation scripts can be found [here](https://github.com/pnnl/ML4AlgComb/tree/master/symmetric_group_character).
+
+- **Repository:** [ACD Repo](https://github.com/pnnl/ML4AlgComb/tree/master/weaving_patterns)
+  
+## Uses
+
+This dataset was generated to study ML model's ability yield insight on an open 
+problem in algebraic combinatorics, specifically, the problem of better understanding commutation 
+equivalent representations of reduced words coresponding to the longest permutation.
+
+### Direct Use
+
+We use this dataset for a classification task distinguishing between weaving and non-weaving patterns.
+
+### Out-of-Scope Use
+
+None.
+
+## Dataset Structure
+
+Each matrix is stored on a single line in row-major format. For instance,
+
+`(0, 1, 2, 3, 3, 2, 3, 4, 2, 3, 2, 1, 5, 4, 3, 2)`
+
+## Dataset Creation
+
+Data generation scripts can be found 
+[here](https://github.com/pnnl/ML4AlgComb/tree/master/weaving_patterns).
+
+### Curation Rationale
+
+This dataset was generated as a test of current AI system's ability to advance 
+research mathematics.
+
+#### Who are the source data producers?
+
+Herman Chau wrote code to generate this dataset.
+
+## Bias, Risks, and Limitations
+
+We only provide data for weaving patterns of size \\(6 \times 5\\) and \\(7 \times 6\\) in this repository. 
+We are happy to generate (subsets) of datasets for larger values of \\(n \times n-1\)).
+
+## Citation
+
+**BibTeX:**
+
+
+    @article{chau2025machine,
+        title={Machine learning meets algebraic combinatorics: A suite of datasets capturing research-level conjecturing ability in pure mathematics},
+        author={Chau, Herman and Jenne, Helen and Brown, Davis and He, Jesse and Raugas, Mark and Billey, Sara and Kvinge, Henry},
+        journal={arXiv preprint arXiv:2503.06366},
+        year={2025}
+    }
+
+
+**APA:**
+
+Chau, H., Jenne, H., Brown, D., He, J., Raugas, M., Billey, S., & Kvinge, H. (2025). Machine learning meets algebraic combinatorics: A suite of datasets capturing research-level conjecturing ability in pure mathematics. arXiv preprint arXiv:2503.06366.
+
+## Dataset Card Contact
+
+Henry Kvinge, acdbenchdataset@gmail.com
+
+## References
+
+\[1\] Felsner, Stefan. "On the number of arrangements of pseudolines." Proceedings of the twelfth annual Symposium on Computational Geometry. 1996.
+\[2\] Chau, Herman. "On enumerating higher bruhat orders through deletion and contraction." arXiv preprint arXiv:2412.10532 (2024).