$(-1)$–Enumeration of Self–Complementary Plane Partitions

Abstract

We prove a product formula for the remaining cases of the weighted enumeration of self–complementary plane partitions contained in a given box where adding one half of an orbit of cubes and removing the other half of the orbit changes the sign of the weight. We use nonintersecting lattice path families to express this enumeration as a Pfaffian which can be expressed in terms of the known ordinary enumeration of self–complementary plane partitions.