Matchings in Corona graph and classical symmetric varieties

2025/05/07 by Ya-Ping Li, Li, Yau Wing
Mathematics · Computer Science · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2505.04581

Abstract

We introduce an alternative combinatorial parametrization of Borel orbits in classical symmetric varieties using matchings of the Corona graph. As an application, we obtain ultra log-concavity and unimodality for the number of Borel orbits in Types AIII and CII. Moreover, we prove a conjecture of Can and Ugurlu concerning the non-integrality of the coefficients of the polynomial that interpolates the number of orbits in Type BI.

Citations

• The genesis of involutions (polarizations and lattice paths)
• Symmetric subgroup orbit closures on flag varieties: Their equivariant\n geometry, combinatorics, and connections with degeneracy loci

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