{
  "id": "0802.0572",
  "version": "v2",
  "published": "2008-02-05T10:18:10.000Z",
  "updated": "2008-05-02T07:26:38.000Z",
  "title": "On the number of collinear triples in permutations",
  "authors": [
    "Liangpan Li"
  ],
  "comment": "4 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\alpha:\\mathbb{Z}_n\\to\\mathbb{Z}_n$ be a permutation and $\\Psi(\\alpha)$ be the number of collinear triples modulo $n$ in the graph of $\\alpha$. Cooper and Solymosi had given by induction the bound $\\min_{\\alpha}\\Psi(\\alpha)\\geq\\lceil(n-1)/4\\rceil$ when $n$ is a prime number. The main purpose of this paper is to give a direct proof of that bound. Besides, the expected number of collinear triples a permutation can have is also been determined.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-05-02T07:26:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51E15",
      "11T99"
    ],
    "keywords": [
      "permutation",
      "collinear triples modulo",
      "direct proof",
      "prime number",
      "main purpose"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.0572L"
    }
  }
}