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Juan B. Gil ; Oscar A. Lopez ; Michael D. Weiner - A positional statistic for 1324-avoiding permutations

dmtcs:12629 - Discrete Mathematics & Theoretical Computer Science, November 4, 2024, vol. 26:1, Permutation Patterns 2023 - https://doi.org/10.46298/dmtcs.12629
A positional statistic for 1324-avoiding permutationsArticle

Authors: Juan B. Gil ; Oscar A. Lopez ; Michael D. Weiner

    We consider the class Sn(1324) of permutations of size n that avoid the pattern 1324 and examine the subset Sann(1324) of elements for which an[a1], a1. This notation means that, when written in one line notation, such a permutation must have a to the left of n, and the elements of {1,,a1} must all be to the right of n. For n2, we establish a connection between the subset of permutations in S1nn(1324) having the 1 adjacent to the n (called primitives), and the set of 1324-avoiding dominoes with n2 points. For a{1,2}, we introduce constructive algorithms and give formulas for the enumeration of Sann(1324) by the position of a relative to the position of n. For a3, we formulate some conjectures for the corresponding generating functions.


    Volume: vol. 26:1, Permutation Patterns 2023
    Section: Special issues
    Published on: November 4, 2024
    Accepted on: September 17, 2024
    Submitted on: December 1, 2023
    Keywords: Mathematics - Combinatorics,05A05

    Classifications

    Mathematics Subject Classification 20201

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