Tannock, Murray and Ulfarsson, Henning - Equivalence classes of mesh patterns with a dominating pattern

dmtcs:3283 - Discrete Mathematics & Theoretical Computer Science, February 9, 2018, Vol. 19 no. 2, Permutation Patterns 2016
Equivalence classes of mesh patterns with a dominating pattern

Authors: Tannock, Murray and Ulfarsson, Henning

Two mesh patterns are coincident if they are avoided by the same set of permutations, and are Wilf-equivalent if they have the same number of avoiders of each length. We provide sufficient conditions for coincidence of mesh patterns, when only permutations also avoiding a longer classical pattern are considered. Using these conditions we completely classify coincidences between families containing a mesh pattern of length 2 and a classical pattern of length 3. Furthermore, we completely Wilf-classify mesh patterns of length 2 inside the class of 231-avoiding permutations.


Source : oai:arXiv.org:1704.07104
Volume: Vol. 19 no. 2, Permutation Patterns 2016
Section: Permutation Patterns
Published on: February 9, 2018
Submitted on: April 25, 2017
Keywords: Mathematics - Combinatorics,05A05, 05A15


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