Geometry of totally symmetric plane partitions (TSPPs) with self-conjugate main diagonal

Abstract

We show that a cyclically symmetric plane partition with selfconjugate main diagonal must be a TSPP and that any TSPP with self-conjugate main diagonal is uniquely determined by that diagonal. We also indicate by means of an example how this latter proof yields an algorithm for recovering the TSPP from its diagonal. The following generating functions are developed. Namely: 1. A generating function for all TSPPs with self-conjugate main diagonal; 2. The generating function for 1-shell TSPPs (defined later).