{
  "id": "1106.2315",
  "version": "v1",
  "published": "2011-06-12T14:48:37.000Z",
  "updated": "2011-06-12T14:48:37.000Z",
  "title": "Set families with a forbidden induced subposet",
  "authors": [
    "Edward Boehnlein",
    "Tao Jiang"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "For each poset $H$ whose Hasse diagram is a tree of height $k$, we show that the largest size of a family $\\cF$ of subsets of $[n]=\\{1,..., n\\}$ not containing $H$ as an induced subposet is asymptotic to $(k-1){n\\choose \\fl{n/2}}$. This extends the result of Bukh \\cite{bukh}, which in turn generalizes several known results including Sperner's theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-12T14:48:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05"
    ],
    "keywords": [
      "forbidden induced subposet",
      "set families",
      "hasse diagram",
      "turn generalizes",
      "sperners theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.2315B"
    }
  }
}