Coincidence among families of mesh patterns

Anders Claesson, Bridget Eileen Tenner, Henning Ulfarsson

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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
Pages (from-to)88-106
Number of pages19
JournalAustralasian Journal of Combinatorics
Issue number1
Publication statusPublished - 20 Aug 2015

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