Descent distribution on Catalan words avoiding a pattern of length at most three

Jean-Luc Baril (1, 2) , Sergey Kirgizov Kirgizov (1, 2) , Vincent Vajnovszki (1, 2)

1 Le2i - Laboratoire Electronique, Informatique et Image [UMR6306]
2 Le2i - Laboratoire d'Electronique, d'Informatique et d'Image [EA 7508]

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 x(n)y(k) in its series expansion is the number of length n p-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. (C) 2018 Elsevier B.V. All rights reserved.

Mots clés: Catalan word; Pattern avoidance; Descent; Popularity

Domaines: Mathématiques [math]

Jean-Luc Baril, Sergey Kirgizov Kirgizov, Vincent Vajnovszki. Descent distribution on Catalan words avoiding a pattern of length at most three. Discrete Mathematics, 2018, 341 (9), pp.2608 - 2615. ⟨10.1016/j.disc.2018.06.001⟩. ⟨hal-01923911⟩