Work

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

Year: 2025

Type: article

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 a b -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.

Source: Advances in Mathematics

DOI: 10.1016/j.aim.2025.110618

Author: Christian Stump

Institution: Ruhr University Bochum

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,790

Funder: Deutsche Forschungsgemeinschaft