Mesh patterns with superfluous mesh

2013/02/07 by Bridget Eileen Tenner, Tenner, Bridget Eileen · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Primary: 05A05 #Secondary: 05A15 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1302.1883

openalex publication_date 2013/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Mesh patterns are a generalization of classical permutation patterns that encompass classical, bivincular, Bruhat-restricted patterns, and some barred patterns. In this paper, we describe all mesh patterns whose avoidance is coincident with classical avoidance, in a sense declaring that the additional data of a mesh was unnecessary for these patterns. We also describe the permutations having the fewest superfluous meshes, and the permutations having the most, enumerating the superfluous meshes in each case.

Cited by

• Enumeration of polyominoes defined in terms of pattern avoidance or convexity constraints

Related

• Distributions of several infinite families of mesh patterns
• Combinatorics of simple marked mesh patterns in 132-avoiding permutations
• Mesh patterns and the expansion of permutation statistics as sums of permutation patterns
• Algorithmic coincidence classification of mesh patterns
• Coincidental pattern avoidance