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(-1)-enumeration of plane partitions with complementation symmetry

Theresia Eisenkölbl
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Abstract

We compute the weighted enumeration of plane partitions contained in a given box with complementation symmetry where adding one half of an orbit of cubes and removing the other half of the orbit changes the weight by -1 as proposed by Kuperberg. We use nonintersecting lattice path families to accomplish this for transpose-complementary, cyclically symmetric transpose-complementary and totally symmetric self-complementary plane partitions. For symmetric transpose-complementary and self-complementary plane partitions we get partial results. We also describe Kuperberg's proof for the case of cyclically symmetric self-complementary plane partitions.

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Theresia Eisenkölbl. 2002-12-11. (-1)-enumeration of plane partitions with complementation symmetry. https://arxiv.org/abs/math/0011175

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