Popularity of patterns over d-equivalence classes of words and permutations

11/12/2019

∙

by   Jean-Luc Baril, et al.

∙

Université de Bourgogne

∙

0

∙

share

Two same length words are d-equivalent if they have same descent set and same underlying alphabet. In particular, two same length permutations are d-equivalent if they have same descent set. The popularity of a pattern in a set of words is the overall number of copies of the pattern within the words of the set. We show the far-from-trivial fact that two patterns are d-equivalent if and only if they are equipopular over any d-equivalence class, and this equipopularity does not follow obviously from a trivial equidistribution.