Results 111 to 120 of about 176,018 (136)
Shape-Wilf-equivalence is not closed under inversion
We show that shape-Wilf-equivalence is not closed under inversion: of the seven inverse pairs of length-four patterns, exactly one is shape-Wilf-equivalent, and it is precisely the pair generated by the known equivalences of Backelin-West-Xin and Stankova-West. Since inverse patterns are always Wilf-equivalent and lifting commutes with inversion, every
openaire +1 more source
The 4,755 Wilf-equivalence classes of permutations of length eight
Vatter's Question 3.1 asks how many Wilf-equivalence classes of length-eight permutations exist. Alex Dobner answered the question in a personal note posted in March 2026: there are exactly 4,755 classes. This deposit is an independent, fully audited confirmation and citable record: the paper (PDF) plus the complete machine-readable certificate archive
openaire +1 more source
Wilf-equivalence for singleton classes [PDF]
Advances in Applied Mathematics, 2007 Given \(n\) and a permutation matrix \(M\) of rank less than \(n\), how many \(n \times n\) permutation matrices do \textit{not} have \(M\) as a submatrix? Letting \(S_n(M)\) be the set of \(n \times n\) permutation matrices not admitting \(M\) as a submatrix, we want \(| S_n(M)| \).
Guoce Xin, Julian West
exaly +3 more sources
A new class of multiset Wilf equivalent pairs [PDF]
Discrete Mathematics, 2007 Let \(M\) be a multiset. A pair of patterns \((\sigma,\tau)\) is called multiset Wilf equivalent if, for any \(M\), the number of permutations of \(M\) that avoid \(\sigma\) is equal to the number of permutations of \(M\) that avoid \(\tau\). In this paper the author shows that if \(\sigma_{n-2}\) is a permutation of \(\{1^{x_1}, 2^{x_2},\dots, (n-2 ...
Venkateswaran, Vidya
exaly +5 more sources
On refinements of wilf-equivalence for involutions
Journal of Algebraic Combinatorics, 2023 Let $\mathcal{S}_n(π)$ (resp. $\mathcal{I}_n(π)$ and $\mathcal{AI}_n(π)$) denote the set of permutations (resp. involutions and alternating involutions) of length $n$ which avoid the permutation pattern $π$. For $k,m\geq 1$, Backelin-West-Xin proved that $|\mathcal{S}_n(12\cdots kτ)|= |\mathcal{S}_n(k\cdots 21τ)|$ by establishing a bijection between ...
Robin Dapao Zhou, Sherry H F Yan
exaly +3 more sources
Refined Wilf-equivalences by Comtet statistics
Electronic Research Archive, 2021 39 pages, 2 tables, 2 figures.
Shishuo Fu, Zhicong Lin
exaly +6 more sources
Rook and Wilf equivalence of integer partitions [PDF]
European Journal of Combinatorics, 2018 27, European Journal of Combinatorics ...
Jonathan Bloom
exaly +5 more sources