{
  "id": "0808.3114",
  "version": "v1",
  "published": "2008-08-22T16:54:37.000Z",
  "updated": "2008-08-22T16:54:37.000Z",
  "title": "Top homology of hypergraph matching complexes, $p$-cycle complexes and Quillen complexes of symmetric groups",
  "authors": [
    "John Shareshian",
    "Michelle L Wachs"
  ],
  "comment": "25 pages",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "We investigate the representation of a symmetric group $S_n$ on the homology of its Quillen complex at a prime $p$. For homology groups in small codimension, we derive an explicit formula for this representation in terms of the representations of symmetric groups on homology groups of $p$-uniform hypergraph matching complexes. We conjecture an explicit formula for the representation of $S_n$ on the top homology group of the corresponding hypergraph matching complex when $n \\equiv 1 \\bmod p$. Our conjecture follows from work of Bouc when $p=2$, and we prove the conjecture when $p=3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-08-22T16:54:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D30",
      "05E25"
    ],
    "keywords": [
      "symmetric group",
      "cycle complexes",
      "quillen complexes",
      "homology group",
      "representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.3114S"
    }
  }
}