Results 11 to 20 of about 114,014 (293)
Pattern avoidance in parking functions [PDF]
Enumerative Combinatorics and Applications, 2023 In this paper, we view parking functions viewed as labeled Dyck paths in order to study a notion of pattern avoidance first introduced by Remmel and Qiu. In particular we enumerate the parking functions avoiding any set of two or more patterns of length 3, and we obtain a number of well-known combinatorial sequences as a result.
Ayomikun Adeniran, Lara Pudwell
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Avoidability of Palindrome Patterns [PDF]
The Electronic Journal of Combinatorics, 2021 We characterize the formulas that are avoided by every $\alpha$-free word for some $\alpha>1$. We show that the avoidable formulas whose fragments are of the form $XY$ or $XYX$ are $4$-avoidable. The largest avoidability index of an avoidable palindrome pattern is known to be at least $4$ and at most $16$. We make progress toward the conjecture that
Ochem, Pascal, Rosenfeld, Matthieu
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Pattern-avoiding permutation powers [PDF]
Discrete Mathematics, 2020 Recently, B na and Smith defined strong pattern avoidance, saying that a permutation $ $ strongly avoids a pattern $ $ if $ $ and $ ^2$ both avoid $ $. They conjectured that for every positive integer $k$, there is a permutation in $S_{k^3}$ that strongly avoids $123\cdots (k+1)$.
Amanda Burcroff, Colin Defant
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Pattern-avoiding polytopes [PDF]
European Journal of Combinatorics, 2018 Two well-known polytopes whose vertices are indexed by permutations in the symmetric group $\mathfrak{S}_n$ are the permutohedron $P_n$ and the Birkhoff polytope $B_n$. We consider polytopes $P_n(Π)$ and $B_n(Π)$, whose vertices correspond to the permutations in $\mathfrak{S}_n$ avoiding a set of patterns $Π$. For various choices of $Π$, we explore the
Robert Davis, Bruce Sagan
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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 ...
Chen, William Y. C. +2 more
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Large sets avoiding patterns [PDF]
Analysis & PDE, 2018 We construct subsets of Euclidean space of large Hausdorff dimension and full Minkowski dimension that do not contain nontrivial patterns described by the zero sets of functions. The results are of two types. Given a countable collection of $v$-variate vector-valued functions $f_q : (\mathbb{R}^{n})^v \to \mathbb{R}^m$ satisfying a mild regularity ...
Fraser, Robert, Pramanik, Malabika
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On Pattern-Avoiding Partitions [PDF]
The Electronic Journal of Combinatorics, 2008 A set partition of size $n$ is a collection of disjoint blocks $B_1,B_2,\ldots$, $B_d$ whose union is the set $[n]=\{1,2,\ldots,n\}$. We choose the ordering of the blocks so that they satisfy $\min B_1 < \min B_2 < \cdots < \min B_d$. We represent such a set partition by a canonical sequence $\pi_1,\pi_2,\ldots,\pi_n$, with $\pi_i=j$ if $i\in ...
Jelínek, Vít, Mansour, Toufik
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Permutations Avoiding a Simsun Pattern [PDF]
The Electronic Journal of Combinatorics, 2020 A permutation $\pi$ avoids the simsun pattern $\tau$ if $\pi$ avoids the consecutive pattern $\tau$ and the same condition applies to the restriction of $\pi$ to any interval $[k].$ Permutations avoiding the simsun pattern $321$ are the usual simsun permutation introduced by Simion and Sundaram.
Barnabei, Marilena +3 more
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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 $n$.
Gunby, Benjamin, Fishelson, Maxwell
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Pattern Avoidance in Poset Permutations [PDF]
Order, 2015 We extend the concept of pattern avoidance in permutations on a totally ordered set to pattern avoidance in permutations on partially ordered sets. The number of permutations on $P$ that avoid the pattern $π$ is denoted $Av_P(π)$. We extend a proof of Simion and Schmidt to show that $Av_P(132) \leq Av_P(123)$ for any poset $P$, and we exactly classify ...
Hopkins, Samuel Francis, Weiler, Morgan
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