2023/02/24 by Baril, Jean-Luc, Ramírez, José Luis · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2302.12741
This work is a continuation of some recent articles presenting enumerative results for Catalan words avoiding one or a pair of consecutive or classical patterns of length 3. More precisely, we provide systematically the bivariate generating function for the number of Catalan words avoiding a given pair of relations with respect to the length and the number of descents. We also present several constructive bijections preserving the number of descents. As a byproduct, we deduce the generating function for the total number of descents on all Catalan words of a given length and avoiding a pair of ordered relations.