Distribution of mesh patterns

     The notion of a mesh pattern, generalizing several classes of permutation patterns, was introduced in 2011 by Branden and Claesson to provide explicit expansions for certain permutation statistics as, possibly infinite, linear combinations of (classical) permutation patterns. There is a long line of research papers dedicated to the study of mesh patterns and their generalizations.
    In this talk, I will discuss a systematic study of avoidance and distribution of mesh patterns of short length, and also some other more general results.