The equivalence between enumerating cyclically symmetric, self-complementary and totally symmetric, self-complementary plane partitions
Mihai Ciucu
Abstract
We prove that the number of cyclically symmetric, self-complementary plane partitions contained in a cube of side 2n equals the square of the number of totally symmetric, self-complementary plane partitions contained in the same cube, without explicitly evaluating either of these numbers. This appears to be the first direct proof of this fact. The problem of finding such a proof was suggested by Stanley.
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