Jean-Luc Baril ; Carine Khalil ; Vincent Vajnovszki - Catalan words avoiding pairs of length three patterns

dmtcs:6002 - Discrete Mathematics & Theoretical Computer Science, April 16, 2021, vol. 22 no. 2, Permutation Patterns 2019
Catalan words avoiding pairs of length three patterns

Authors: Jean-Luc Baril ; Carine Khalil ; Vincent Vajnovszki

Catalan words are particular growth-restricted words counted by the eponymous integer sequence. In this article we consider Catalan words avoiding a pair of patterns of length 3, pursuing the recent initiating work of the first and last authors and of S. Kirgizov where (among other things) the enumeration of Catalan words avoiding a patterns of length 3 is completed. More precisely, we explore systematically the structural properties of the sets of words under consideration and give enumerating results by means of recursive decomposition, constructive bijections or bivariate generating functions with respect to the length and descent number. Some of the obtained enumerating sequences are known, and thus the corresponding results establish new combinatorial interpretations for them.


Volume: vol. 22 no. 2, Permutation Patterns 2019
Section: Special issues
Published on: April 16, 2021
Submitted on: December 25, 2019
Keywords: Computer Science - Discrete Mathematics,Mathematics - Combinatorics


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