A Catalan Subset of Descending Plane Partitions

Research paper by Colton Keller, Jessica Striker

Indexed on: 19 Apr '17Published on: 19 Apr '17Published in: arXiv - Mathematics - Combinatorics


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.