2018/03/18 by Jean-Luc Baril, Baril, Jean-Luc, Sergey Kirgizov +3 · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Coding theory and cryptography #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1803.06706
openalex publication_date 2018/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Catalan words are particular growth-restricted words over the set of\nnon-negative integers, and they represent still another combinatorial class\ncounted by the Catalan numbers. We study the distribution of descents on the\nsets of Catalan words avoiding a pattern of length at most three: for each such\na pattern p we provide a bivariate generating function where the coefficient\nof xnyk in its series expansion is the number of length n Catalan words\nwith k descents and avoiding p. As a byproduct, we enumerate the set of\nCatalan words avoiding p, and we provide the popularity of descents on this\nset. Some of the obtained enumerating sequences are not yet recorded in the\nOn-line Encyclopedia of Integer Sequences.\n