Involutions of the Symmetric Group and Congruence B-orbits of Anti-Symmetric Matrices

Details Involutions of the Symmetric Group and Congruence B-orbits of Anti-Symmetric Matrices Involutions of the Symmetric Group and Congruence B-orbits of Anti-Symmetric Matrices

2009-10-25

arxiv.org/abs/0910.4743v1

Mathematics

Combinatorics

Scientific paper

We present the poset of Borel congruence classes of anti-symmetric matrices
ordered by containment of closures. We show that there exists a bijection
between the set of these classes and the set of involutions of the symmetric
group. We give two formulas for the rank function of this poset.

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