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The Chow and augmented Chow polynomials of uniform matroids

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arxiv 2410.22329 v2 pith:3KAZK647 submitted 2024-10-29 math.CO

classification math.CO
keywords chowmatroidsformulasaugmentedcombinatorialpolynomialschubertuniform
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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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