Multiplicative partition functions for reverse plane partitions derived from an integrable dynamical system
Combinatorics
2017-01-25 v1
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.
Cite
@article{arxiv.1701.06762,
title = {Multiplicative partition functions for reverse plane partitions derived from an integrable dynamical system},
author = {Shuhei Kamioka},
journal= {arXiv preprint arXiv:1701.06762},
year = {2017}
}