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Matchings Avoiding Partial Patterns [PDF]
The Electronic Journal of Combinatorics, 2006 We show that matchings avoiding a certain partial pattern are counted by the $3$-Catalan numbers. We give a characterization of $12312$-avoiding matchings in terms of restrictions on the corresponding oscillating tableaux. We also find a bijection between matchings avoiding both patterns $12312$ and $121323$ and Schröder paths without peaks at level ...
William Y. C. Chen +2 more
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Pattern-avoiding permutation powers [PDF]
Discrete Mathematics, 2020 16 pages, 1 ...
Amanda Burcroff, Colin Defant
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Pattern Avoidance Over a Hypergraph [PDF]
The Electronic Journal of Combinatorics, 2021 A classic result of Marcus and Tardos (previously known as the Stanley-Wilf conjecture) bounds from above the number of $n$-permutations ($\sigma \in S_n$) that do not contain a specific sub-permutation. In particular, it states that for any fixed permutation $\pi$, the number of $n$-permutations that avoid $\pi$ is at most exponential in $n$.
Benjamin Gunby, Maxwell Fishelson
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Pattern Avoidance in Ascent Sequences [PDF]
The Electronic Journal of Combinatorics, 2011 Ascent sequences are sequences of nonnegative integers with restrictions on the size of each letter, depending on the number of ascents preceding it in the sequence. Ascent sequences have recently been related to $(2+2)$-free posets and various other combinatorial structures.
Duncan, Paul, Steingrimsson, Einar
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On Pattern Avoiding Indecomposable Permutations [PDF]
Integers, 2016 Comtet introduced the notion of indecomposable permutations in 1972. A permutation is indecomposable if and only if it has no proper prefix which is itself a permutation. Indecomposable permutations were studied in the literature in various contexts.
Gao, Alice L. L. +2 more
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Pattern classes of permutations via bijections between linearly ordered sets [PDF]
, 2008 A pattern class is a set of permutations closed under pattern involvement or, equivalently, defined by certain subsequence avoidance conditions. Any pattern class X which is atomic, i.e.
Ruskuc, Nikola +3 more
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Generalized permutation patterns - a short survey [PDF]
, 2010 An occurrence of a classical pattern p in a permutation π is a subsequence of π whose letters are in the same relative order (of size) as those in p.
Steingrimsson, Einar
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Advances in Applied Mathematics, 2012 We extend the notion of consecutive pattern avoidance to considering sums over all permutations where each term is a product of weights depending on each consecutive pattern of a fixed length. We study the problem of finding the asymptotics of these sums. Our technique is to extend the spectral method of Ehrenborg, Kitaev and Perry.
Richard Ehrenborg, JiYoon Jung
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Pattern avoidance by palindromes
Theoretical Computer Science, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
I. A. Mikhailova, Mikhail V. Volkov 0001
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Pattern avoidance of generalized permutations [PDF]
Advances in Applied Mathematics, 2019 In this paper, we study pattern avoidances of generalized permutations and show that the number of all generalized permutations avoiding $π$ is independent of the choice of $π\in S_3$, which extends the classic results on permutations avoiding $π\in S_3$.
Zhousheng Mei, Suijie Wang
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