Volume Polynomials and Log-concavity of the Characteristic Polynomials of Matroids

Eric Katz

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arXiv · 2508.08391

Volume Polynomials and Log-concavity of the Characteristic Polynomials of Matroids

Eric Katz

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Abstract

The Rota--Heron--Welsh conjecture (now a theorem of Adiprasito, Huh, and the author) asserts the log-concavity of the characteristic polynomial of matroids. We give an exposition of the Lorentzian polynomial proof following the work of Branden and Leake aimed at undergraduate and beginning graduate students.

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Eric Katz. 2025-08-11. Volume Polynomials and Log-concavity of the Characteristic Polynomials of Matroids. https://arxiv.org/abs/2508.08391

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