Joseph Johnson: Plane partitions of rectangle and trapezoid shape

Abstract: A plane partition (or P-partition) is a nonnegative integer labeling of a poset which weakly increases as you travel up the edges of the poset. In 1983 Proctor showed that the rectangle poset and its associated trapezoid poset have the same number of plane partitions with maximum label k for each nonnegative integer k. We give a bijective proof of this result. Our bijection arises from a piecewise-linear, volume-preserving, and continuous map between order polytopes, which distinguishes it from the only other known bijection. This talk is based on joint work with Ricky Liu.