PERMUTATION ENUMERATION OF THE SYMMETRICAL GROUP AND THE COMBINATORICS OF SYMMETRICAL FUNCTIONS

In a recent paper, Brenti shows that enumerating a conjugacy class of S-n with respect to excedances produces polynomials which are unimodal and symmetric. He then shows that these polynomials arise naturally from the theory of symmetric functions. We give combinatorial proofs of Brenti's results; our combinatorial methods lead to numerous extensions, as well as to the definition of new combinatorial objects-border rim hook tabloids. (C) 1995 Academic Press, Inc.