A Catalan Subset of Descending Plane Partitions

2017/04/19 by Colton Keller, Jessica Striker, Keller, Colton +1
Computer Science · Mathematics · #05A15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1704.05779

openalex publication_date 2017/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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