Bruhat Order on Partial Fixed Point Free Involutions
Keywords: Bruhat-Chevalley order, partial fixed-point-free involutions, EL-shellability, rank-generating function.
AbstractThe order complex of inclusion poset $PF_n$ of Borel orbit closures in skew-symmetric matrices is investigated. It is shown that $PF_n$ is an EL-shellable poset, and furthermore, its order complex triangulates a ball. The rank-generating function of $PF_n$ is computed and the resulting polynomial is contrasted with the Hasse-Weil zeta function of the variety of skew-symmetric matrices over finite fields.