Hanna Mularczyk - Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations

dmtcs:6494 - Discrete Mathematics & Theoretical Computer Science, August 31, 2021, vol. 22 no. 2, Permutation Patterns 2019 - https://doi.org/10.46298/dmtcs.6494
Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations

Authors: Hanna Mularczyk

    Defant, Engen, and Miller defined a permutation to be uniquely sorted if it has exactly one preimage under West's stack-sorting map. We enumerate classes of uniquely sorted permutations that avoid a pattern of length three and a pattern of length four by establishing bijections between these classes and various lattice paths. This allows us to prove nine conjectures of Defant.


    Volume: vol. 22 no. 2, Permutation Patterns 2019
    Section: Special issues
    Published on: August 31, 2021
    Accepted on: April 28, 2021
    Submitted on: May 20, 2020
    Keywords: Mathematics - Combinatorics,05A05, 05A15,G.2.1

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