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  # Dataset Card for Weaving Patterns of Size, \\(6 \times 5\\)
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  *Weaving patterns* are \\((n \times n−1)\\)-matrices with \\(\{1, 2, \dots , n\}\\)-
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- entries introduced by \[1\] to study the number of reduced decompositions of the
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- permutation that swaps \\(n\\) and \\(1\\), \\(n\\) - \\(1\\) and \\(2\\), etc. up to commutation equivalence. The number
 
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  of such objects counts a wide range of combinatorial phenomena, including the number of parallel sorting
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  networks, the number of rhombic tilings of regular polygons, and is connected to
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  the study of the higher Bruhat orders \[2\]. An \\(O(n^2)\\) algorithm for determining
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  - **Repository:** [ACD Repo](https://github.com/pnnl/ML4AlgComb/tree/master/weaving_patterns)
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- ## Uses
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-
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- This dataset was generated to study ML model's ability yield insight on an open
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- problem in algebraic combinatorics, specifically, the problem of better understanding commutation
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- equivalent representations of reduced words coresponding to the longest permutation.
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-
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- ### Direct Use
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-
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- We use this dataset for a classification task distinguishing between weaving and non-weaving patterns.
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-
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- ### Out-of-Scope Use
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- None.
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-
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- ## Dataset Structure
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-
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- Each matrix is stored on a single line in row-major format (see example above).
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-
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- ## Dataset Creation
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-
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- Data generation scripts can be found
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- [here](https://github.com/pnnl/ML4AlgComb/tree/master/weaving_patterns).
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-
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- ### Curation Rationale
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- This dataset was generated as a test of current AI system's ability to advance
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- research mathematics.
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-
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- #### Who are the source data producers?
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- Herman Chau wrote code to generate this dataset.
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-
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- ## Bias, Risks, and Limitations
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- We only provide data for weaving patterns of size \\(6 \times 5\\) and \\(7 \times 6\\) in this repository.
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- We are happy to generate (subsets) of datasets for larger values of \\(n \times n-1\)).
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-
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  ## Citation
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  **BibTeX:**
 
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  # Dataset Card for Weaving Patterns of Size, \\(6 \times 5\\)
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  *Weaving patterns* are \\((n \times n−1)\\)-matrices with \\(\{1, 2, \dots , n\}\\)-
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+ entries introduced by \[1\] to study the number of reduced decompositions of the longest
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+ permutation (which swaps \\(n\\) and \\(1\\), \\(n\\) - \\(1\\) and \\(2\\), etc.) up
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+ to commutation equivalence. The number
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  of such objects counts a wide range of combinatorial phenomena, including the number of parallel sorting
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  networks, the number of rhombic tilings of regular polygons, and is connected to
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  the study of the higher Bruhat orders \[2\]. An \\(O(n^2)\\) algorithm for determining
 
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  - **Repository:** [ACD Repo](https://github.com/pnnl/ML4AlgComb/tree/master/weaving_patterns)
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  ## Citation
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  **BibTeX:**