Permutation enumeration symmetric functions, and unimodality

Francesco Brenti

Vol. 157 (1993), No. 1, 1–28

DOI: 10.2140/pjm.1993.157.1

Abstract

We study the polynomials obtained by enumerating a set of permutations with respect to the number of excedances. We prove that these polynomials have only real zeros and are unimodal for many interesting classes of permutations. We then show how these polynomials also arise naturally from the theory of symmetric functions.

Mathematical Subject Classification 2000

Primary: 05E05

Secondary: 05A05, 05A17

Milestones

Received: 12 March 1991

Revised: 26 November 1991

Published: 1 January 1993