{
  "id": "1104.2519",
  "version": "v2",
  "published": "2011-04-13T14:51:29.000Z",
  "updated": "2012-02-15T02:10:43.000Z",
  "title": "Log-concavity of characteristic polynomials and the Bergman fan of matroids",
  "authors": [
    "June Huh",
    "Eric Katz"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-02-15T02:10:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bergman fan",
      "log-concavity",
      "intersection problems",
      "coefficients",
      "hodge type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.2519H"
    }
  }
}