Bruhat order on partial fixed point free involutions

Mahir Bilen Can; Yonah Cherniavsky; Tim Twelbeck

doi:10.37236/4396

Bruhat order on partial fixed point free involutions

Mahir Bilen Can, Yonah Cherniavsky, Tim Twelbeck

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English
Article number	P4.34
Journal	Electronic Journal of Combinatorics
Volume	21
Issue number	4
DOIs	https://doi.org/10.37236/4396
State	Published - 13 Nov 2014

Keywords

Bruhat-Chevalley order
EL-shellability
Partial fixed-point-free involutions
Rank generating function

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10.37236/4396

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abstract = "The order complex of inclusion poset PFn of Borel orbit closures in skew-symmetric matrices is investigated. It is shown that PFn is an EL-shellable poset, and furthermore, its order complex triangulates a ball. The rank-generating function of PFn is computed and the resulting polynomial is contrasted with the Hasse-Weil zeta function of the variety of skew-symmetric matrices over finite fields.",

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N2 - The order complex of inclusion poset PFn of Borel orbit closures in skew-symmetric matrices is investigated. It is shown that PFn is an EL-shellable poset, and furthermore, its order complex triangulates a ball. The rank-generating function of PFn is computed and the resulting polynomial is contrasted with the Hasse-Weil zeta function of the variety of skew-symmetric matrices over finite fields.

AB - The order complex of inclusion poset PFn of Borel orbit closures in skew-symmetric matrices is investigated. It is shown that PFn is an EL-shellable poset, and furthermore, its order complex triangulates a ball. The rank-generating function of PFn is computed and the resulting polynomial is contrasted with the Hasse-Weil zeta function of the variety of skew-symmetric matrices over finite fields.

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KW - Rank generating function

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Bruhat order on partial fixed point free involutions

Abstract

Keywords

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