English

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}
}
R2 v1 2026-06-22T19:25:25.065Z