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Chow polynomials of uniform matroids are real-rooted
Published Web Location
https://doi.org/10.5070/C66165702Abstract
June Huh and Matthew Stevens conjectured that the Hilbert-Poincaré series of the Chow ring of any matroid is a polynomial with only real zeros. We prove this conjecture for the class of uniform matroids. We also prove that the Chow polynomial and the augmented Chow polynomial of any maximal ranked poset have only real zeros. Mathematics Subject Classifications: 05E14, 05B35, 06A07, 26C10 Keywords: Chow polynomials, real-rooted polynomials, partially ordered sets, geometric lattices