Distributions of mesh patterns of short lengths on king permutations

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-07-16 DOI:10.1016/j.disc.2025.114681

Dan Li, Philip B. Zhang

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引用次数: 0

Abstract

Brändén and Claesson introduced the concept of mesh patterns in 2011, and since then, these patterns have attracted significant attention in the literature. Subsequently, in 2015, Hilmarsson et al. initiated the first systematic study of avoidance of mesh patterns, while Kitaev and Zhang conducted the first systematic study of the distribution of mesh patterns in 2019. A permutation

σ = σ_{1} σ_{2} \dots σ_{n}

in the symmetric group

S_{n}

is called a king permutation if

| σ_{i + 1} - σ_{i} | > 1

for each

1 \leq i \leq n - 1

. Riordan derived a recurrence relation for the number of such permutations in 1965. The generating function for king permutations was obtained by Flajolet and Sedgewick in 2009. In this paper, we initiate a systematic study of the distribution of mesh patterns on king permutations by finding distributions for 22 mesh patterns of short lengths.

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王排列上短长度网状图案的分布

Brändén和Claesson在2011年引入了网格模式的概念，从那时起，这些模式在文献中引起了极大的关注。随后，Hilmarsson等人在2015年首次对网格模式的回避进行了系统研究，Kitaev和Zhang于2019年首次对网格模式的分布进行了系统研究。对称群Sn中的排列σ=σ1σ2⋯σn称为王排列，如果|σi+1−σi|>；1对于每个1≤i≤n−1。Riordan在1965年推导出了这种排列数目的递归关系。king置换的生成函数由Flajolet和Sedgewick在2009年得到。在本文中，我们通过寻找22种短长度网格模式的分布，对王排列上网格模式的分布进行了系统的研究。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.