Equivalence classes of mesh patterns with a dominating pattern

Discrete Mathematics & Theoretical Computer Science, February 9, 2018, Vol. 19 no. 2, Permutation Patterns 2016

Murray and Henning

An equivalence 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.

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