{
  "id": "math/0512598",
  "version": "v3",
  "published": "2005-12-27T12:46:12.000Z",
  "updated": "2007-12-15T18:12:51.000Z",
  "title": "On partitions of the unit interval generated by Brocot sequences",
  "authors": [
    "Anna Dushistova"
  ],
  "comment": "36 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $ p_{i, n}, i=1,..., N(n)=2^{n-1} $ be the lengths of intervals between the neighboring fractions of Brocot sequence $ F_n $. We obtain an asymptotic formula for $\\sigma_{\\beta}(F_n)=\\sum_{i=1}^{N(n)} p_{i, n}^{\\beta} $,which improves known estimates.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-12-15T18:12:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B99"
    ],
    "keywords": [
      "unit interval",
      "brocot sequence",
      "partitions",
      "asymptotic formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12598D"
    }
  }
}