Distributions of several infinite families of mesh patterns

Sergey Kitaev, Philip B. Zhang, Xutong Zhang

Research output: Contribution to journalArticle

Abstract

Brändén and Claesson introduced mesh patterns to provide explicit expansions for certain permutation statistics as linear combinations of (classical) permutation patterns. The first systematic study of the avoidance of mesh patterns was conducted by Hilmarsson et al., while the first systematic study of the distribution of mesh patterns was conducted by the first two authors. In this paper, we provide far-reaching generalizations for 8 known distribution results and 5 known avoidance results related to mesh patterns by giving distribution or avoidance formulas for certain infinite families of mesh patterns in terms of distribution or avoidance formulas for smaller patterns. Moreover, as a corollary to a general result, we find the distribution of one more mesh pattern of length 2.

Original languageEnglish
Article number124984
Number of pages15
JournalApplied Mathematics and Computation
Volume372
Early online date2 Jan 2020
DOIs
Publication statusPublished - 1 May 2020

Keywords

  • mesh patterns
  • permutation patterns
  • linear combinations

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