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arXiv · 1508.02975

Permutation totally symmetric self-complementary plane partitions

Jessica Striker
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Abstract

Alternating sign matrices and totally symmetric self-complementary plane partitions are equinumerous sets of objects for which no explicit bijection is known. In this paper, we identify a subset of totally symmetric self-complementary plane partitions corresponding to permutations by giving a statistic-preserving bijection to permutation matrices, which are a subset of alternating sign matrices. We use this bijection to define a new partial order on permutations, and prove this new poset contains both the Tamari lattice and the Catalan distributive lattice as subposets. We also study a new partial order on totally symmetric self-complementary plane partitions arising from this perspective and show that this is a distributive lattice related to Bruhat order when restricted to permutations.

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Jessica Striker. 2018-05-24. Permutation totally symmetric self-complementary plane partitions. https://arxiv.org/abs/1508.02975

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