Coincidence among families of mesh patterns

Anders Claesson, Bridget Eileen Tenner, Henning Ulfarsson

Research output: Working paper

Abstract

Two mesh patterns are coincident if they are avoided by the same set of permutations. In this paper, we provide necessary conditions for this coincidence, which include having the same set of enclosed diagonals. This condition is sufficient to prove coincidence of vincular patterns, although it is not enough to guarantee coincidence of bivincular patterns. In addition, we provide a generalization of the Shading Lemma (Hilmarsson et al.), a result that examined when a square could be added to the mesh of a pattern.
LanguageEnglish
Place of PublicationUnited States
Number of pages17
Publication statusPublished - 25 May 2016

Fingerprint

Coincidence
Mesh
Shading
Coincident
Lemma
Permutation
Sufficient
Necessary Conditions
Family

Keywords

  • discrete mathematics
  • mesh patterns
  • pattern coincidence

Cite this

Claesson, A., Tenner, B. E., & Ulfarsson, H. (2016). Coincidence among families of mesh patterns. United States.
Claesson, Anders ; Tenner, Bridget Eileen ; Ulfarsson, Henning. / Coincidence among families of mesh patterns. United States, 2016.
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abstract = "Two mesh patterns are coincident if they are avoided by the same set of permutations. In this paper, we provide necessary conditions for this coincidence, which include having the same set of enclosed diagonals. This condition is sufficient to prove coincidence of vincular patterns, although it is not enough to guarantee coincidence of bivincular patterns. In addition, we provide a generalization of the Shading Lemma (Hilmarsson et al.), a result that examined when a square could be added to the mesh of a pattern.",
keywords = "discrete mathematics, mesh patterns, pattern coincidence",
author = "Anders Claesson and Tenner, {Bridget Eileen} and Henning Ulfarsson",
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Claesson, A, Tenner, BE & Ulfarsson, H 2016 'Coincidence among families of mesh patterns' United States.

Coincidence among families of mesh patterns. / Claesson, Anders; Tenner, Bridget Eileen; Ulfarsson, Henning.

United States, 2016.

Research output: Working paper

TY - UNPB

T1 - Coincidence among families of mesh patterns

AU - Claesson, Anders

AU - Tenner, Bridget Eileen

AU - Ulfarsson, Henning

PY - 2016/5/25

Y1 - 2016/5/25

N2 - Two mesh patterns are coincident if they are avoided by the same set of permutations. In this paper, we provide necessary conditions for this coincidence, which include having the same set of enclosed diagonals. This condition is sufficient to prove coincidence of vincular patterns, although it is not enough to guarantee coincidence of bivincular patterns. In addition, we provide a generalization of the Shading Lemma (Hilmarsson et al.), a result that examined when a square could be added to the mesh of a pattern.

AB - Two mesh patterns are coincident if they are avoided by the same set of permutations. In this paper, we provide necessary conditions for this coincidence, which include having the same set of enclosed diagonals. This condition is sufficient to prove coincidence of vincular patterns, although it is not enough to guarantee coincidence of bivincular patterns. In addition, we provide a generalization of the Shading Lemma (Hilmarsson et al.), a result that examined when a square could be added to the mesh of a pattern.

KW - discrete mathematics

KW - mesh patterns

KW - pattern coincidence

UR - http://arxiv.org/abs/1412.0703

UR - http://arxiv.org/

M3 - Working paper

BT - Coincidence among families of mesh patterns

CY - United States

ER -

Claesson A, Tenner BE, Ulfarsson H. Coincidence among families of mesh patterns. United States. 2016 May 25.