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arXiv · 2406.18932

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

Christian Stump
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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.

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Christian Stump. 2025-10-20. Chow and augmented Chow polynomials as evaluations of Poincaré-extended ab-indices. https://arxiv.org/abs/2406.18932

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