Consecutive patterns in Catalan words and the descent distribution

Abstract In this paper, we compute the distribution of descent statistic on Catalan words avoiding a consecutive pattern length at most three. Baril–Kirgizov–Vajnovszki began study patterns in words, focusing enumeration those that avoid classical 3. We make use symbolic method to associate functional equations satisfied by counting generating functions. As consequence enumerate set 3, and also provide total number descents set.