{
  "id": "1311.6291",
  "version": "v2",
  "published": "2013-11-25T13:24:12.000Z",
  "updated": "2015-11-12T13:51:01.000Z",
  "title": "A generalization of weight polynomials to matroids",
  "authors": [
    "Trygve Johnsen",
    "Jan Roksvold",
    "Hugues Verdure"
  ],
  "comment": "21 pages",
  "doi": "10.1016/j.disc.2015.10.005",
  "categories": [
    "math.CO"
  ],
  "abstract": "Generalizing polynomials previously studied in the context of linear codes, we define weight polynomials and an enumerator for a matroid $M$. Our main result is that these polynomials are determined by Betti numbers associated with graded minimal free resolutions of the Stanley-Reisner ideals of $M$ and so-called elongations of $M$. Generalizing Greene's theorem from coding theory, we show that the enumerator of a matroid is equivalent to its Tutte polynomial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-25T13:24:12.000Z",
      "abstract": "Generalizing polynomials previously studied in the context of linear codes, we define weight polynomials and an enumerator for a matroid M. Our main result is that both of these polynomials are determined by Betti numbers associated to the Stanley-Reisner ideals of M and so-called elongations of M. Also, we show that Betti tables of elongations of M are partly determined by the Betti table of M. Generalizing a known result in coding theory, we show that the enumerator of a matroid is equivalent to its Tutte polynomial, and vice versa.",
      "comment": "24 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-11-12T13:51:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35",
      "13D02",
      "94B05"
    ],
    "keywords": [
      "generalization",
      "define weight polynomials",
      "betti table",
      "elongations",
      "vice versa"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.6291J"
    }
  }
}