Results 1 to 10 of about 176,018 (136)
Descent c-Wilf Equivalence [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 Let $S_n$ denote the symmetric group. For any $\sigma \in S_n$, we let $\mathrm{des}(\sigma)$ denote the number of descents of $\sigma$, $\mathrm{inv}(\sigma)$ denote the number of inversions of $\sigma$, and $\mathrm{LRmin}(\sigma)$ denote the number of
Quang T. Bach, Jeffrey B. Remmel
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The 26 Wilf-equivalence classes of length five quasi-consecutive patterns [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 We present two families of Wilf-equivalences for consecutive and quasi-consecutive vincular patterns. These give new proofs of the classification of consecutive patterns of length $4$ and $5$.
Evan Chen, Shyam Narayanan
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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
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Refined Wilf-equivalences by Comtet statistics
Electronic Research Archive, 2021 39 pages, 2 tables, 2 figures.
Shishuo Fu, Zhicong Lin
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Rook and Wilf equivalence of integer partitions [PDF]
European Journal of Combinatorics, 2018 27, European Journal of Combinatorics ...
Jonathan Bloom
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Wilf equivalence relations for consecutive patterns [PDF]
Advances in Applied Mathematics, 2018 Two permutations $π$ and $τ$ are c-Wilf equivalent if, for each $n$, the number of permutations in $S_n$ avoiding $π$ as a consecutive pattern (i.e., in adjacent positions) is the same as the number of those avoiding $τ$. In addition, $π$ and $τ$ are strongly c-Wilf equivalent if, for each $n$ and $k$, the number of permutations in $S_n$ containing $k$
Sergi Elizalde
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Rationality, irrationality, and Wilf equivalence in generalized factor order [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Let $P$ be a partially ordered set and consider the free monoid $P^{\ast}$ of all words over $P$. If $w,w' \in P^{\ast}$ then $w'$ is a factor of $w$ if there are words $u,v$ with $w=uw'v$. Define generalized factor order on $P^{\ast}$ by letting $u \leq
Sergey Kitaev +3 more
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On (shape-)Wilf-equivalence for words [PDF]
Advances in Applied Mathematics, 2018 AmS-LaTeX, 13 pages; minor ...
Christian Krattenthaler
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Wilf equivalences between vincular patterns in inversion sequences [PDF]
Applied Mathematics and Computation, 2021 18 pages, 9 ...
Sergi Elizalde
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Operators of equivalent sorting power and related Wilf-equivalences [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We study sorting operators $\textrm{A}$ on permutations that are obtained composing Knuth's stack sorting operator \textrmS and the reverse operator $\textrm{R}$, as many times as desired.
Michael Albert, Mathilde Bouvel
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