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