{
  "id": "1111.4493",
  "version": "v1",
  "published": "2011-11-18T21:27:32.000Z",
  "updated": "2011-11-18T21:27:32.000Z",
  "title": "An Erdős-Ko-Rado theorem for multisets",
  "authors": [
    "Karen Meagher",
    "Alison Purdy"
  ],
  "comment": "8 pages",
  "journal": "Electron. J. Combin. 18 (2011), no.1, Paper 220, 8 pp",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $k$ and $m$ be positive integers. A collection of $k$-multisets from $\\{1,..., m \\}$ is intersecting if every pair of multisets from the collection is intersecting. We prove that for $m \\geq k+1$, the size of the largest such collection is $\\binom{m+k-2}{k-1}$ and that when $m > k+1$, only a collection of all the $k$-multisets containing a fixed element will attain this bound. The size and structure of the largest intersecting collection of $k$-multisets for $m \\leq k$ is also given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-18T21:27:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05"
    ],
    "keywords": [
      "erdős-ko-rado theorem",
      "largest intersecting collection",
      "positive integers",
      "fixed element"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.4493M"
    }
  }
}