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

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

2000-11-22

arxiv.org/abs/math/0011175v3

Adv. Appl. Math. 30, No. 1-2, 53-95 (2003)

Mathematics

Combinatorics

41 pages, AmS-LaTeX, uses TeXDraw; reference added

Scientific paper

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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