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arXiv · 1704.05779

A Catalan Subset of Descending Plane Partitions

Colton Keller·Jessica Striker
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Abstract

Descending plane partitions, alternating sign matrices, and totally symmetric self-complementary plane partitions are equinumerous combinatorial sets for which no explicit bijection is known. In this paper, we isolate a subset of descending plane partitions counted by the Catalan numbers. The proof follows by constructing a generating tree on these descending plane partitions that has the same structure as the generating tree for 231-avoiding permutations. We hope this result will provide insight on the search for a bijection with alternating sign matrices and/or totally symmetric self-complementary plane partitions, since these also contain Catalan subsets.

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Colton Keller, Jessica Striker. 2017-04-19. A Catalan Subset of Descending Plane Partitions. https://arxiv.org/abs/1704.05779

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