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arXiv:1104.2519

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Title: Log-concavity of characteristic polynomials and the Bergman fan of matroids
Authors: June Huh, Eric Katz
Categories: math.CO Combinatorics (math.AG Algebraic Geometry)
Comments: 12 pages

Abstract: In a recent paper, the first author proved the log-concavity of the coefficients of the characteristic polynomial of a matroid realizable over a field of characteristic 0, answering a long-standing conjecture of Read in graph theory. We extend the proof to all realizable matroids, making progress towards a more general conjecture of Rota-Heron-Welsh. Our proof follows from an identification of the coefficients of the reduced characteristic polynomial as answers to particular intersection problems on a toric variety. The log-concavity then follows from an inequality of Hodge type.

Owner: Eric Katz
Version 1: Wed, 13 Apr 2011 14:51:29 GMT
Version 2: Wed, 15 Feb 2012 02:10:43 GMT

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