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Autor principal: Stump, Christian
Formato: Preprint
Publicado: 2024
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Acceso en línea:https://arxiv.org/abs/2406.18932
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author Stump, Christian
author_facet Stump, Christian
contents 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.
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publishDate 2024
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spellingShingle Chow and augmented Chow polynomials as evaluations of Poincaré-extended ab-indices
Stump, Christian
Combinatorics
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.
title Chow and augmented Chow polynomials as evaluations of Poincaré-extended ab-indices
topic Combinatorics
url https://arxiv.org/abs/2406.18932