{
  "id": "1009.0394",
  "version": "v3",
  "published": "2010-09-02T11:19:18.000Z",
  "updated": "2011-02-07T12:44:55.000Z",
  "title": "Betti numbers of Stanley--Reisner rings with pure resolutions",
  "authors": [
    "Gabor Hegedüs"
  ],
  "comment": "18 pages, better introduction, ask for feedback before submission",
  "categories": [
    "math.CO",
    "math.AC"
  ],
  "abstract": "Let $\\Delta$ be simplicial complex and let $k[\\Delta]$ denote the Stanley--Reisner ring corresponding to $\\Delta$. Suppose that $k[\\Delta]$ has a pure free resolution. Then we describe the Betti numbers and the Hilbert--Samuel multiplicity of $k[\\Delta]$ in terms of the $h$--vector of $\\Delta$. As an application, we derive a linear equation system and some inequalities for the components of the $h$--vector of the clique complex of an arbitrary chordal graph. As an other application, we derive a linear equation system and some inequalities for the components of the $h$--vector of Cohen--Macaulay simplicial complexes.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-02-07T12:44:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E40",
      "13D02",
      "13D40"
    ],
    "keywords": [
      "betti numbers",
      "pure resolutions",
      "stanley-reisner ring",
      "linear equation system",
      "cohen-macaulay simplicial complexes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.0394H"
    }
  }
}