Coincidence among families of mesh patterns
The Australasian Journal of Combinatorics 2015, Volume 63 Part 1 (2015)
Two mesh patterns are coincident if they are avoided by the same set of
permutations. In this paper, we provide necessary conditions for this
coincidence, which include having the same set of enclosed diagonals. This
condition is sufficient to prove coincidence of vincular patterns, although it
is not enough to guarantee coincidence of bivincular patterns. In addition, we
provide a generalization of the Shading Lemma (Hilmarsson et al.), a result
that examined when a square could be added to the mesh of a pattern.