{
  "id": "math/0306119",
  "version": "v1",
  "published": "2003-06-06T12:52:00.000Z",
  "updated": "2003-06-06T12:52:00.000Z",
  "title": "The number of k-intersections of an intersecting family of r-sets",
  "authors": [
    "John Talbot"
  ],
  "comment": "10 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Erdos-Ko-Rado theorem tells us how large an intersecting family of r-sets from an n-set can be, while results due to Lovasz and Tuza give bounds on the number of singletons that can occur as pairwise intersections of sets from such a family. We consider a natural generalization of these problems. Given an intersecting family of r-sets from an n-set and 1\\leq k \\leq r, how many k-sets can occur as pairwise intersections of sets from the family? For k=r and k=1 this reduces to the problems described above. We answer this question exactly for all values of k and r, when n is sufficiently large. We also characterize the extremal families.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-06-06T12:52:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05"
    ],
    "keywords": [
      "intersecting family",
      "k-intersections",
      "erdos-ko-rado theorem tells",
      "pairwise intersections",
      "extremal families"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......6119T"
    }
  }
}