{
  "id": "1001.0313",
  "version": "v3",
  "published": "2010-01-04T18:58:23.000Z",
  "updated": "2010-11-29T01:28:08.000Z",
  "title": "Erdos-Ko-Rado theorems for simplicial complexes",
  "authors": [
    "Russ Woodroofe"
  ],
  "comment": "14 pages; v2 has minor changes; v3 has further minor changes for publication",
  "journal": "J. Combin. Theory Ser. A 118 (2011), no. 4, 1218-1227",
  "doi": "10.1016/j.jcta.2010.11.022",
  "categories": [
    "math.CO"
  ],
  "abstract": "A recent framework for generalizing the Erdos-Ko-Rado Theorem, due to Holroyd, Spencer, and Talbot, defines the Erdos-Ko-Rado property for a graph in terms of the graph's independent sets. Since the family of all independent sets of a graph forms a simplicial complex, it is natural to further generalize the Erdos-Ko-Rado property to an arbitrary simplicial complex. An advantage of working in simplicial complexes is the availability of algebraic shifting, a powerful shifting (compression) technique, which we use to verify a conjecture of Holroyd and Talbot in the case of sequentially Cohen-Macaulay near-cones.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-11-29T01:28:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E45",
      "05D05"
    ],
    "keywords": [
      "erdos-ko-rado theorem",
      "simplicial complexes",
      "erdos-ko-rado property",
      "graphs independent sets",
      "arbitrary simplicial complex"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.0313W"
    }
  }
}