Multipartite P-partitions and inner products of skew Schur functions. (English) Zbl 0562.05007

Gessel, Ira M.

Combinatorics and algebra, Proc. Conf., Boulder/Colo. 1983, Contemp. Math. 34, 289-301 (1984).

[For the entire collection see Zbl 0546.00008.]
A generalization of Stanley’s theory of P-partitions to multipartite partitions is developed, which is used to count r-tuples of permutations whose product is a given permutation according to their descent sets. The theory gives a combinatorial interpretation to numbers associated with inner products of certain skew Schur functions.

Reviewer: J.Cigler

MSC:

05A17	Combinatorial aspects of partitions of integers
05A10	Factorials, binomial coefficients, combinatorial functions

Keywords:

P-partitions; multipartite partitions; skew Schur functions