Involutions of the Symmetric Group and Congruence B-orbits of Anti-Symmetric Matrices
classification
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keywords
anti-symmetricclassescongruencegroupinvolutionsmatricesposetsymmetric
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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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