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The 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.

Bruhat Order on Partial Fixed Point Free Involutions