Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902902 | Discrete Mathematics | 2018 | 8 Pages |
Abstract
Catalan words are particular growth-restricted words over the set of non-negative integers, and they represent still another combinatorial class counted by the Catalan numbers. We study the distribution of descents on the sets of Catalan words avoiding a pattern of length at most three: for each such a pattern p we provide a bivariate generating function where the coefficient of xnyk in its series expansion is the number of length np-avoiding Catalan words with k descents. As a byproduct, we enumerate the set of Catalan words avoiding p, and we provide the popularity of descents on this set.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Jean-Luc Baril, Sergey Kirgizov, Vincent Vajnovszki,