{
  "id": "1106.2944",
  "version": "v4",
  "published": "2011-06-15T11:35:58.000Z",
  "updated": "2013-06-10T16:56:57.000Z",
  "title": "Matroids and log-concavity",
  "authors": [
    "Matthias Lenz"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "We show that f-vectors of matroid complexes of realisable matroids are log-concave. This was conjectured by Mason in 1972. Our proof uses the recent result by Huh and Katz who showed that the coefficients of the characteristic polynomial of a realisable matroid form a log-concave sequence. We also discuss the relationship between log-concavity of f-vectors and h-vectors of matroids. In the last section we explain the connection between zonotopal algebra and f-vectors and characteristic polynomials of matroids.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-06-10T16:56:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A20",
      "05B35",
      "05E45",
      "05C31"
    ],
    "keywords": [
      "log-concavity",
      "characteristic polynomial",
      "log-concave sequence",
      "realisable matroid form",
      "matroid complexes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.2944L"
    }
  }
}