2000/11/30 by Theresia Eisenkölbl
Mathematics · #math.CO #msc:05A15 #msc:05A19 #msc:05B45 #msc:33C20 #msc:52C20
published as Adv. Appl. Math. 30, No. 1-2, 53-95 (2003) · 41 pages, AmS-LaTeX, uses TeXDraw; reference added
arxiv created 2002/12/11 · arxiv updated 2009/11/30
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.