Coincidence among families of mesh patterns

Anders Claesson, Bridget Eileen Tenner, Henning Ulfarsson

Research output: Working paper

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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.
Original languageEnglish
Place of PublicationUnited States
Number of pages17
Publication statusPublished - 25 May 2016

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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.