The equivalence between enumerating cyclically symmetric, self-complementary and totally symmetric, self-complementary plane partitions

Details The equivalence between enumerating cyclically symmetric, self-complementary and totally symmetric, self-complementary plane partitions The equivalence between enumerating cyclically symmetric, self-complementary and totally symmetric, self-complementary plane partitions

1998-08-04

arxiv.org/abs/math/9808019v1

Mathematics

Combinatorics

Scientific paper

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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