Séminaire Lotharingien de Combinatoire, 78B.29 (2017), 12 pp.
Multiplicative Partition Functions for Reverse Plane Partitions Derived from an Integrable Dynamical System
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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