A Bump Statistic on Permutations Resulting from the Robinson–Schensted Correspondence

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Annals of Combinatorics Pub Date : 2024-07-08 DOI:10.1007/s00026-024-00708-z

Mark Dukes, Andrew Mullins

引用次数: 0

Abstract

In this paper, we investigate a permutation statistic that was independently introduced by Romik (Funct Anal Appl 39(2):52–155, 2005). This statistic counts the number of bumps that occur during the execution of the Robinson–Schensted procedure when applied to a given permutation. We provide several interpretations of this bump statistic that include the tableaux shape and also as an extremal problem concerning permutations and increasing subsequences. Several aspects of this bump statistic are investigated from both structural and enumerative viewpoints.

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罗宾逊-申斯泰德对应关系产生的排列的凹凸统计量

在本文中，我们研究了罗米克（Funct Anal Appl 39(2):52-155, 2005）独立提出的一种置换统计量。这个统计量统计的是罗宾逊-申斯泰德程序在应用于给定排列时发生的碰撞次数。我们对凹凸统计量做了几种解释，其中包括表格形状，也包括关于排列和递增子序列的极值问题。我们从结构和枚举的角度研究了凹凸统计量的几个方面。

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

Annals of Combinatorics 数学-应用数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Annals of Combinatorics publishes outstanding contributions to combinatorics with a particular focus on algebraic and analytic combinatorics, as well as the areas of graph and matroid theory. Special regard will be given to new developments and topics of current interest to the community represented by our editorial board. The scope of Annals of Combinatorics is covered by the following three tracks: Algebraic Combinatorics: Enumerative combinatorics, symmetric functions, Schubert calculus / Combinatorial Hopf algebras, cluster algebras, Lie algebras, root systems, Coxeter groups / Discrete geometry, tropical geometry / Discrete dynamical systems / Posets and lattices Analytic and Algorithmic Combinatorics: Asymptotic analysis of counting sequences / Bijective combinatorics / Univariate and multivariable singularity analysis / Combinatorics and differential equations / Resolution of hard combinatorial problems by making essential use of computers / Advanced methods for evaluating counting sequences or combinatorial constants / Complexity and decidability aspects of combinatorial sequences / Combinatorial aspects of the analysis of algorithms Graphs and Matroids: Structural graph theory, graph minors, graph sparsity, decompositions and colorings / Planar graphs and topological graph theory, geometric representations of graphs / Directed graphs, posets / Metric graph theory / Spectral and algebraic graph theory / Random graphs, extremal graph theory / Matroids, oriented matroids, matroid minors / Algorithmic approaches