{
  "id": "0812.4562",
  "version": "v1",
  "published": "2008-12-24T20:08:45.000Z",
  "updated": "2008-12-24T20:08:45.000Z",
  "title": "Shellable Complexes from Multicomplexes",
  "authors": [
    "Jonathan Browder"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Suppose a group $G$ acts properly on a simplicial complex $\\Gamma$. Let $l$ be the number of $G$-invariant vertices and $p_1, p_2, ... p_m$ be the sizes of the $G$-orbits having size greater than 1. Then $\\Gamma$ must be a subcomplex of $\\Lambda = \\Delta^{l-1}* \\partial \\Delta^{p_1-1}*... * \\partial \\Delta^{p_m-1}$. A result of Novik gives necessary conditions on the face numbers of Cohen-Macaulay subcomplexes of $\\Lambda$. We show that these conditions are also sufficient, and thus provide a complete characterization of the face numbers of these complexes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-12-24T20:08:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E99"
    ],
    "keywords": [
      "shellable complexes",
      "multicomplexes",
      "face numbers",
      "invariant vertices",
      "simplicial complex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.4562B"
    }
  }
}