Equivalence classes of mesh patterns with a dominating pattern
Combinatorics
2023-06-22 v4
Abstract
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.
Keywords
Cite
@article{arxiv.1704.07104,
title = {Equivalence classes of mesh patterns with a dominating pattern},
author = {Murray Tannock and Henning Ulfarsson},
journal= {arXiv preprint arXiv:1704.07104},
year = {2023}
}