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arXiv · 2410.22329

The Chow and augmented Chow polynomials of uniform matroids

Elena Hoster
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Abstract

We provide explicit combinatorial formulas for the Chow polynomial and for the augmented Chow polynomial of uniform matroids, thereby proving a conjecture by Ferroni. These formulas refine existing formulas by Hampe and by Eur, Huh, and Larson, offering a combinatorial interpretation of the coefficients based on Schubert matroids. As a byproduct, we count Schubert matroids by rank, number of loops, and cogirth.

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Elena Hoster. 2024-11-29. The Chow and augmented Chow polynomials of uniform matroids. https://arxiv.org/abs/2410.22329

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