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

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