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 - https://doi.org/10.46298/dmtcs.6002
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
    Accepted on: April 1, 2021
    Submitted on: December 25, 2019
    Keywords: Computer Science - Discrete Mathematics,Mathematics - Combinatorics

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    Source : ScholeXplorer HasVersion DOI 10.48550/arxiv.1912.10447
    • 10.48550/arxiv.1912.10447
    Catalan words avoiding pairs of length three patterns
    Baril, Jean-Luc ; Khalil, Carine ; Vajnovszki, Vincent ;

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