Congruence B-Orbits and the Bruhat Poset of Involutions of the Symmetric Group
arXiv:0912.1819
Abstract
We study the poset of Borel congruence classes of symmetric matrices ordered by containment of closures. We give a combinatorial description of this poset and calculate its rank function. We discuss the relation between this poset and the Bruhat poset of involutions of the symmetric group.