{
  "id": "0902.2444",
  "version": "v1",
  "published": "2009-02-14T09:29:17.000Z",
  "updated": "2009-02-14T09:29:17.000Z",
  "title": "A combinatorial proof of a formula for Betti numbers of a stacked polytope",
  "authors": [
    "Suyoung Choi",
    "Jang Soo Kim"
  ],
  "comment": "7 pages",
  "journal": "Electron. J. Combin., 17(1), #R9, 2010",
  "categories": [
    "math.CO",
    "math.AC"
  ],
  "abstract": "For a simplicial complex $\\Delta$, the graded Betti number $\\beta_{i,j}(k[\\Delta])$ of the Stanley-Reisner ring $k[\\Delta]$ over a field $k$ has a combinatorial interpretation due to Hochster. Terai and Hibi showed that if $\\Delta$ is the boundary complex of a $d$-dimensional stacked polytope with $n$ vertices for $d\\geq3$, then $\\beta_{k-1,k}(k[\\Delta])=(k-1)\\binom{n-d}{k}$. We prove this combinatorially.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-14T09:29:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "52B05"
    ],
    "keywords": [
      "combinatorial proof",
      "dimensional stacked polytope",
      "graded betti number",
      "combinatorial interpretation",
      "simplicial complex"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.2444C"
    }
  }
}