✦ LIBER ✦

The Equivalence between Enumerating Cyclically Symmetric, Self-Complementary and Totally Symmetric, Self-Complementary Plane Partitions

✍ Scribed by Mihai Ciucu

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 142 KB
Volume: 86
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1998.2922

No coin nor oath required. For personal study only.

✦ Synopsis

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 (J. Combin. Theory Ser. A 43 (1996), 103 113).