{
  "id": "1906.06657",
  "version": "v1",
  "published": "2019-06-16T07:15:31.000Z",
  "updated": "2019-06-16T07:15:31.000Z",
  "title": "Hypergraphs without exponents",
  "authors": [
    "Zoltán Füredi",
    "Dániel Gerbner"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Here we give a short, concise proof for the following result. There exists a $k$-uniform hypergraph $H$ (for $k\\geq 5$) without exponent, i.e., when the Tur\\'an function is not polynomial in $n$. More precisely, we have $ex(n,H)=o(n^{k-1})$ but it exceeds $n^{k-1-c}$ for any positive $c$ for $n> n_0(k,c)$. This is an extension (and simplification) of a result of Frankl and the first author from 1987 where the case $k=5$ was proven. We conjecture that it is true for $k\\in \\{3, 4\\}$ as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-16T07:15:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "concise proof",
      "uniform hypergraph",
      "turan function",
      "first author",
      "polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}