Jessica Striker ; Nathan Williams - Promotion and Rowmotion

dmtcs:3038 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) - https://doi.org/10.46298/dmtcs.3038
Promotion and Rowmotion

Authors: Jessica Striker ; Nathan Williams ORCID-iD

    We present an equivariant bijection between two actions—promotion and rowmotion—on order ideals in certain posets. This bijection simultaneously generalizes a result of R. Stanley concerning promotion on the linear extensions of two disjoint chains and certain cases of recent work of D. Armstrong, C. Stump, and H. Thomas on noncrossing and nonnesting partitions. We apply this bijection to several classes of posets, obtaining equivariant bijections to various known objects under rotation. We extend the same idea to give an equivariant bijection between alternating sign matrices under rowmotion and under B. Wieland's gyration. Lastly, we define two actions with related orders on alternating sign matrices and totally symmetric self-complementary plane partitions.


    Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
    Section: Proceedings
    Published on: January 1, 2012
    Imported on: January 31, 2017
    Keywords: poset, order ideal, noncrossing, promotion, equivariant, alternating sign matrices,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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    Source : ScholeXplorer IsReferencedBy ARXIV 1507.00249
    Source : ScholeXplorer IsReferencedBy DOI 10.1017/fms.2017.5
    Source : ScholeXplorer IsReferencedBy DOI 10.48550/arxiv.1507.00249
    • 1507.00249
    • 10.1017/fms.2017.5
    • 10.1017/fms.2017.5
    • 10.1017/fms.2017.5
    • 10.48550/arxiv.1507.00249
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