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arXiv · 1803.06706

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

Jean-Luc Baril·Sergey Kirgizov·Vincent Vajnovszki
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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 $x^ny^k$ in its series expansion is the number of length $n$ Catalan words with $k$ descents and avoiding $p$. As a byproduct, we enumerate the set of Catalan words avoiding $p$, and we provide the popularity of descents on this set. Some of the obtained enumerating sequences are not yet recorded in the On-line Encyclopedia of Integer Sequences.

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Jean-Luc Baril, Sergey Kirgizov, Vincent Vajnovszki. 2018-03-18. Descent distribution on Catalan words avoiding a pattern of length at most three. https://arxiv.org/abs/1803.06706

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