Equivalence classes of mesh patterns with a dominating pattern

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

Equivalence classes of mesh patterns with a dominating pattern

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