Bruhat Order on Partial Fixed Point Free Involutions
Copyright policy )Bruhat Order on Partial Fixed Point Free Involutions
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.
- Tulane University United States
- Ariel University Israel
Algebraic systems of matrices, EL-shellability, Algebraic aspects of posets, skew-symmetric matrices, Bruhat-Chevalley order, Combinatorial aspects of groups and algebras, Combinatorics of partially ordered sets, FOS: Mathematics, Linear algebraic groups over the reals, the complexes, the quaternions, Mathematics - Combinatorics, partial fixed-point-free involutions, Combinatorics (math.CO), Classical groups (algebro-geometric aspects), rank-generating functions
Algebraic systems of matrices, EL-shellability, Algebraic aspects of posets, skew-symmetric matrices, Bruhat-Chevalley order, Combinatorial aspects of groups and algebras, Combinatorics of partially ordered sets, FOS: Mathematics, Linear algebraic groups over the reals, the complexes, the quaternions, Mathematics - Combinatorics, partial fixed-point-free involutions, Combinatorics (math.CO), Classical groups (algebro-geometric aspects), rank-generating functions
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