Striker, Jessica and Williams, Nathan - 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)
Promotion and Rowmotion

Authors: Striker, Jessica and Williams, Nathan

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
Submitted 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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