Wenjie Fang - Bijective proof of a conjecture on unit interval posets

dmtcs:10837 - Discrete Mathematics & Theoretical Computer Science, February 23, 2024, vol. 26:2 - https://doi.org/10.46298/dmtcs.10837
Bijective proof of a conjecture on unit interval posetsArticle

Authors: Wenjie Fang

    In a recent preprint, Matherne, Morales and Selover conjectured that two different representations of unit interval posets are related by the famous zeta map in $q,t$-Catalan combinatorics. This conjecture was proved recently by GĂ©linas, Segovia and Thomas using induction. In this short note, we provide a bijective proof of the same conjecture with a reformulation of the zeta map using left-aligned colored trees, first proposed in the study of parabolic Tamari lattices.


    Volume: vol. 26:2
    Section: Combinatorics
    Published on: February 23, 2024
    Accepted on: January 30, 2024
    Submitted on: January 20, 2023
    Keywords: Mathematics - Combinatorics

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