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

2009/10/25 by Yonah Cherniavsky, Cherniavsky, Yonah
Mathematics · #05A05 #06A07 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0910.4743

openalex publication_date 2009/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Congruence B-Orbits and the Bruhat Poset of Involutions of the Symmetric Group
• Real and symmetric matrices
• Monoid Embeddings of Symmetric Varieties
• Lexicographic Shellability of Partial Involutions
• Partial order on involutive permutations and double Schubert cells