{
  "id": "1802.03444",
  "version": "v1",
  "published": "2018-02-09T20:39:08.000Z",
  "updated": "2018-02-09T20:39:08.000Z",
  "title": "Using the existence of t-designs to prove Erdős-Ko-Rado",
  "authors": [
    "Chris Godsil",
    "Krystal Guo"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In 1984, Wilson proved the Erd\\H{o}s-Ko-Rado theorem for $t$-intersecting families of $k$-subsets of an $n$-set: he showed that if $n\\ge(t+1)(k-t+1)$ and $\\mathcal{F}$ is a family of $k$-subsets of an $n$-set such that any two members of $\\mathcal{F}$ have at least $t$ elements in common, then $|\\mathcal{F}|\\le\\binom{n-t}{k-t}$. His proof made essential use of a matrix whose origin is not obvious. In this paper we show that this matrix can be derived, in a sense, as a projection of $t$-$(n,k,1)$ design.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-09T20:39:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05",
      "05C50"
    ],
    "keywords": [
      "erdős-ko-rado",
      "intersecting families",
      "projection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}