Séminaire Lotharingien de Combinatoire, 78B.29 (2017), 12 pp.

Shuhei Kamioka

Multiplicative Partition Functions for Reverse Plane Partitions Derived from an Integrable Dynamical System

Abstract. In this paper we clarify a close connection between reverse plane partitions and an integrable dynamical system called the discrete two-dimensional (2D) Toda molecule. We show that a multiplicative partition function for reverse plane partitions of arbitrary shape with bounded parts can be obtained from each non-vanishing solution to the discrete 2D Toda molecule. As an example we derive a partition function which generalizes MacMahon's triple product formula and Gansner's multi-trace generating function from a specific solution to the discrete 2D Toda molecule.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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