Results 11 to 20 of about 116,248 (268)
Consecutive patterns in permutations: clusters and generating functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We use the cluster method in order to enumerate permutations avoiding consecutive patterns. We reprove and generalize in a unified way several known results and obtain new ones, including some patterns of length 4 and 5, as well as some infinite families
Sergi Elizalde, Marc Noy
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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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Deodhar Elements in Kazhdan-Lusztig Theory [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 The Kazhdan-Lusztig polynomials for finite Weyl groups arise in representation theory as well as the geometry of Schubert varieties. It was proved very soon after their introduction that they have nonnegative integer coefficients, but no simple all ...
Brant Jones
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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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Discrete Mathematics & Theoretical Computer Science, 2014 A general lattice theoretic construction of Reading constructs Hopf subalgebras of the Malvenuto-Reutenauer Hopf algebra (MR) of permutations. The products and coproducts of these Hopf subalgebras are defined extrinsically in terms of the embedding in MR.
Shirley Law
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Alternating, Pattern-Avoiding Permutations [PDF]
The Electronic Journal of Combinatorics, 2009 We study the problem of counting alternating permutations avoiding collections of permutation patterns including $132$. We construct a bijection between the set $S_n(132)$ of $132$-avoiding permutations and the set $A_{2n + 1}(132)$ of alternating, $132$-avoiding permutations. For every set $p_1, \ldots, p_k$ of patterns and certain related patterns $
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Permutations Avoiding Certain Partially-Ordered Patterns [PDF]
The Electronic Journal of Combinatorics, 2021 A permutation $\pi$ contains a pattern $\sigma$ if and only if there is a subsequence in $\pi$ with its letters in the same relative order as those in $\sigma$. Partially ordered patterns (POPs) provide a convenient way to denote patterns in which the relative order of some of the letters does not matter.
Yap, Kai Ting Keshia +2 more
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Crucial abelian k-power-free words [PDF]
Discrete Mathematics & Theoretical Computer Science, 2010 Combinatorics
Amy Glen +2 more
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