Multiplicative partition functions for reverse plane partitions derived from an integrable dynamical system

TL;DR

This paper establishes a link between reverse plane partitions and the discrete 2D Toda molecule, deriving a multiplicative partition function that generalizes classical formulas using solutions to an integrable system.

Contribution

It introduces a novel method to obtain partition functions for reverse plane partitions from solutions of an integrable dynamical system, extending classical results.

Findings

Derived a multiplicative partition function from the discrete 2D Toda molecule

Generalized MacMahon's triple product formula

Connected reverse plane partitions with integrable systems

Abstract

A close connection of reverse plane partitions with an integrable dynamical system called the discrete two-dimensional (2D) Toda molecule is clarified. It is shown that a multiplicative partition function for reverse plane partition of arbitrary shape with bounded parts can be obtained from each non-vanishing solution to the discrete 2D Toda molecule. As an example a partition function which generalizes MacMahon's triple product formula as well as Gansner's multi-trace generating function is derived from a specific solution to the dynamical system.