(−1)–enumeration of Plane Partitions with Complementation Symmetry
نویسنده
چکیده
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 in [7, pp.25/26]. 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 and for cyclically symmetric self–complementary plane partitions we have a conjecture.
منابع مشابه
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