Congruence B-Orbits and the Bruhat Poset of Involutions of the Symmetric Group

2009/12/09 by Eli Bagno, Bagno, Eli, Yonah Cherniavsky +1
Mathematics · #05A05 #20B30 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0912.1819

openalex publication_date 2009/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the poset of Borel congruence classes of symmetric matrices ordered by containment of closures. We give a combinatorial description of this poset and calculate its rank function. We discuss the relation between this poset and the Bruhat poset of involutions of the symmetric group.

Related

• Involutions of the Symmetric Group and Congruence B-orbits of Anti-Symmetric Matrices
• The Bruhat Order on Symmetric Groups via Intrinsic Coverings of Compositions
• Lexicographic Shellability of Partial Involutions
• The Bruhat order on conjugation-invariant sets of involutions in the symmetric group
• Bruhat Order on Partial Fixed Point Free Involutions