{
  "id": "1204.4423",
  "version": "v3",
  "published": "2012-04-19T18:05:38.000Z",
  "updated": "2013-04-19T10:05:18.000Z",
  "title": "On Possible Turan Densities",
  "authors": [
    "Oleg Pikhurko"
  ],
  "comment": "32 pages; v3: extra details and explanations added; accepted by Israel J Math",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Tur\\'an density \\pi(H) of a family H of k-graphs is the limit as n tends to infinity of the maximum edge density of an H-free k-graph on n vertices. Let I^k consist of all possible Tur\\'an densities and let F^k be the set of Tur\\'an densities of finite k-graph families. Here we prove that F^k contains every density obtained from an arbitrary finite construction by optimally blowing it up and using recursion inside the specified set of parts. As an application, we show that F^k contains an irrational number for each k\\ge 3. Also, we show that I^k has cardinality of the continuum. In particular, I^k is not equal to F^k.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-04-19T10:05:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05",
      "05C65"
    ],
    "keywords": [
      "turan density",
      "arbitrary finite construction",
      "finite k-graph families",
      "maximum edge density",
      "irrational number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.4423P"
    }
  }
}