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

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 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.
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01923911
Contributeur : Le2i - Université de Bourgogne <>
Soumis le : jeudi 15 novembre 2018 - 15:20:53
Dernière modification le : vendredi 17 juillet 2020 - 14:59:11

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

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