# (-1)-enumeration of self-complementary plane
partitions

## Theresia Eisenkölbl

### 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.
(22 pages)

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