The Chow and augmented Chow polynomials of uniform matroids

2024/10/29 by Elena Hoster, Hoster, Elena · 2 citations
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Advanced Algebra and Logic #Advanced Graph Theory Research

paper · pdf · doi:10.48550/arxiv.2410.22329

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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• On gamma-vectors and Chow polynomials of restrictions of reflection arrangements
• Extending the ab-index

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