Bruhat Order on Partial Fixed Point Free Involutions

2014/03/04 by Can, Mahir Bilen, Cherniavsky, Yonah, Twelbeck, Tim
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1403.0703

Abstract

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.

Related

• Lexicographic shellability of the Bruhat-Chevalley order on\n fixed-point-free involutions
• Congruence B-Orbits and the Bruhat Poset of Involutions of the Symmetric Group
• The Bruhat order on conjugation-invariant sets of involutions in the symmetric group
• Lexicographic Shellability of Partial Involutions
• Fixed points of involutive automorphisms of the Bruhat order