{
  "id": "1811.10503",
  "version": "v1",
  "published": "2018-11-26T16:56:03.000Z",
  "updated": "2018-11-26T16:56:03.000Z",
  "title": "On restricted permutations of $\\{1,\\ldots,n\\}$",
  "authors": [
    "Zhi-Wei Sun"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "In this paper we study permutations of $\\{1,\\ldots,n\\}$ with certain restrictions. In particular, we show that there is a unique permutation $\\pi$ of $\\{1,\\ldots,n\\}$ such that all the numbers $k+\\pi(k)$ ($k=1,\\ldots,n$) are powers of two. We also pose some conjectures for further research; for example, we conjecture that for any integer $n>5$ there is a permutation $\\pi$ of $\\{1,\\ldots,n\\}$ such that $$\\sum_{k=1}^{n-1}\\frac1{\\pi(k)\\pi(k+1)}=1.$$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-26T16:56:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "11B39",
      "11B75",
      "11C20"
    ],
    "keywords": [
      "restricted permutations",
      "unique permutation",
      "study permutations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}