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@@ -5,7 +5,7 @@ pretty_name: Characterizing weaving patterns of size 7 x 6
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  # Dataset Card for Weaving Patterns of Size \\(7 \times 6\\)
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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
@@ -17,7 +17,7 @@ exists but gives no additional insight into the structure of
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  weaving patterns and correspondingly the asymptotics of
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  reduced decompositions. The enumeration of reduced decompositions
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  up to commutation equivalence has been studied by many including
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- Knuth and Stanley. An exact formula is likely out of reach,
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  so asymptotic upper and lower bounds are of great interest.
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  ML models that can detect necessary or sufficient conditions
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  for a matrix to be a valid weaving pattern have the potential
@@ -93,4 +93,6 @@ Henry Kvinge, [email protected]
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  ## References
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  \[1\] Felsner, Stefan. "On the number of arrangements of pseudolines." Proceedings of the twelfth annual Symposium on Computational Geometry. 1996.
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- \[2\] Chau, Herman. "On enumerating higher bruhat orders through deletion and contraction." arXiv preprint arXiv:2412.10532 (2024).
 
 
 
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  # Dataset Card for Weaving Patterns of Size \\(7 \times 6\\)
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+ *Weaving patterns* are size \\(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
11
  to commutation equivalence. The number
 
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  weaving patterns and correspondingly the asymptotics of
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  reduced decompositions. The enumeration of reduced decompositions
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  up to commutation equivalence has been studied by many including
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+ Knuth \[3\] and Stanley \[4\]. An exact formula is likely out of reach,
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  so asymptotic upper and lower bounds are of great interest.
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  ML models that can detect necessary or sufficient conditions
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  for a matrix to be a valid weaving pattern have the potential
 
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  ## References
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  \[1\] Felsner, Stefan. "On the number of arrangements of pseudolines." Proceedings of the twelfth annual Symposium on Computational Geometry. 1996.
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+ \[2\] Chau, Herman. "On enumerating higher bruhat orders through deletion and contraction." arXiv preprint arXiv:2412.10532 (2024).
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+ \[3\] Knuth, Donald E., ed. Axioms and hulls. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992.
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+ \[4\] Stanley, Richard P. "On the number of reduced decompositions of elements of Coxeter groups." European Journal of Combinatorics 5.4 (1984): 359-372.