Tian Han ; Sergey Kitaev - Joint distributions of statistics over permutations avoiding two patterns of length 3

dmtcs:12517 - Discrete Mathematics & Theoretical Computer Science, November 4, 2024, vol. 26:1, Permutation Patterns 2023 - https://doi.org/10.46298/dmtcs.12517
Joint distributions of statistics over permutations avoiding two patterns of length 3Article

Authors: Tian Han ; Sergey Kitaev

    Finding distributions of permutation statistics over pattern-avoiding classes of permutations attracted much attention in the literature. In particular, Bukata et al. found distributions of ascents and descents on permutations avoiding any two patterns of length 3. In this paper, we generalize these results in two different ways: we find explicit formulas for the joint distribution of six statistics (asc, des, lrmax, lrmin, rlmax, rlmin), and also explicit formulas for the joint distribution of four statistics (asc, des, MNA, MND) on these permutations in all cases. The latter result also extends the recent studies by Kitaev and Zhang of the statistics MNA and MND (related to non-overlapping occurrences of ascents and descents) on stack-sortable permutations. All multivariate generating functions in our paper are rational, and we provide combinatorial proofs of five equidistribution results that can be derived from the generating functions.


    Volume: vol. 26:1, Permutation Patterns 2023
    Section: Special issues
    Published on: November 4, 2024
    Accepted on: July 27, 2024
    Submitted on: November 7, 2023
    Keywords: Mathematics - Combinatorics

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