Coincidence among families of mesh patterns

Claesson, Anders and Tenner, Bridget Eileen and Ulfarsson, Henning (2016) Coincidence among families of mesh patterns. Preprint / Working Paper. arXiv.org, United States. (http://arxiv.org/abs/1412.0703)

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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.

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• Item metadata

  Item type:	Monograph(Preprint / Working Paper)
  ID code:	51646
  Dates:	Date Event 25 May 2016 Published
  Subjects:	Science > Mathematics
  Department:	Faculty of Science > Computer and Information Sciences
  Depositing user:	Pure Administrator
  Date deposited:	13 Feb 2015 11:43
  Last modified:	09 Apr 2024 04:39
  Related URLs:	Publisher
  URI:	https://strathprints.strath.ac.uk/id/eprint/51646