Log-concavity of characteristic polynomials and the Bergman fan of matroids

June Huh, Eric Katz

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1103-1116
Number of pages14
JournalMathematische Annalen
Volume354
Issue number3
DOIs
StatePublished - Nov 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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