Peter Paule

The talk reports on recent joint work with G. E. Andrews and C. Schneider (RISC-Linz). One of R. Stanley's conjectures (1986) on plane partitions concerned the enumeration of totally symmetric plane partitions (TSPP). J. Stembridge (1995) turned this into a theorem by making ingenious use of the combinatorics of Pfaffians. Based on a theorem of Okada, Andrews (1990) has set up a collection of sufficiently complicated (multiple) hypergeometric sum identities which, once proved, would validate Stanley's conjecture. Due to recent improvement in symbolic summation methods, Andrews' identities finally could be settled.