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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
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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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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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### Direct Use
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We use this dataset for a classification task distinguishing between weaving and non-weaving patterns.
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### Out-of-Scope Use
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None.
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## Dataset Structure
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Each matrix is stored on a single line in row-major format (see example above).
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## Dataset Creation
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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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### 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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#### Who are the source data producers?
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Herman Chau wrote code to generate this dataset.
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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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## 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:**
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