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We present the poset of Borel congruence classes of anti-symmetric matricesordered by containment of closures. We show that there exists a bijectionbetween the set of these classes and the set of involutions of the symmetricgroup. We give two formulas for the rank function of this poset.

ON INVOLUTIONS OF THE SYMMETRIC GROUP AND CONGRUENCE B-ORBITS OF ANTI-SYMMETRIC MATRICES