Chow and augmented Chow polynomials as evaluations of Poincaré-extended ab-indices

2024/06/27 by Stump, Christian · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.18932

Abstract

We show that Chow polynomials and augmented Chow polynomials of matroids, and more generally of finite graded posets admitting R-labelings, are obtained as evaluations of their Poincaré-extended ab-indices. This implies in particular explicit combinatorial γ-positive expansions for both, providing the first proof of the γ-positivity not relying on the Kähler package for the Chow ring. We then evaluate this expansion to obtain an explicit closed formula for the braid arrangement.

Cited by

• Chow polynomials of rank-uniform labeled posets
• On gamma-vectors and Chow polynomials of restrictions of reflection arrangements

Related

• Extending the ab-index
• The Chow and augmented Chow polynomials of uniform matroids
• Chow functions for partially ordered sets
• Chow polynomials of rank-uniform labeled posets
• The Poincaré-extended ab-index