Shuhei Kamioka
Published 2017-01-24Version 1
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.
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