Results 1 to 10 of about 109 (102)
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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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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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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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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Enumeration of super-strong Wilf equivalence classes of permutations in the generalized factor order [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 Super-strong Wilf equivalence classes of the symmetric group ${\mathcal S}_n$ on $n$ letters, with respect to the generalized factor order, were shown by Hadjiloucas, Michos and Savvidou (2018) to be in bijection with pyramidal sequences of consecutive ...
Ioannis Michos, Christina Savvidou
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Bijections for generalized Wilf equivalences
Enumerative Combinatorics and ApplicationsStarting with an inclusion-exclusion proof of a combinatorial identity, a direct bijection can be produced using recursive subtraction (sometimes with a direct combinatorial description). We apply this method to identities for generalized Wilf equivalences among consecutive patterns in inversion sequences, giving direct bijective proofs of some ...
Melanie Ferreri
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Enumeration of Dumont permutations avoiding certain four-letter patterns [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 In this paper, we enumerate Dumont permutations of the fourth kind avoiding or containing certain permutations of length 4. We also conjecture a Wilf-equivalence of two 4-letter patterns on Dumont permutations of the first kind.
Alexander Burstein, Opel Jones
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The Rearrangement Conjecture [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 The Rearrangement Conjecture states that if two words over $\mathbb{P}$ are Wilf-equivalent in the factor order on $\mathbb{P}^{\ast}$ then they are rearrangements of each other.
Jay Pantone, Vincent Vatter
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Enumeration of Stack-Sorting Preimages via a Decomposition Lemma [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 We give three applications of a recently-proven "Decomposition Lemma," which allows one to count preimages of certain sets of permutations under West's stack-sorting map $s$.
Colin Defant
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On (shape-)Wilf-equivalence for words [PDF]
Advances in Applied Mathematics, 2018 AmS-LaTeX, 13 pages; minor ...
Guo, Ting +2 more
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