The Bruhat Order on the Involutions of the Symmetric Group

Abstract

In this paper we study the partially ordered set of the involutions of the symmetric group S n with the order induced by the Bruhat order of S n. We prove that this is a graded poset, with rank function given by the average of the number of inversions and the number of excedances, and that it is lexicographically shellable, hence Cohen-Macaulay, and Eulerian.