{
  "id": "1207.2984",
  "version": "v4",
  "published": "2012-07-12T14:33:01.000Z",
  "updated": "2013-02-17T06:24:55.000Z",
  "title": "Minoration of the complexity function associated to a translation on the torus",
  "authors": [
    "Nicolas Bédaride",
    "Jean François Bertazzon"
  ],
  "comment": "10 pages. 4 figures",
  "categories": [
    "math.DS",
    "math.CO"
  ],
  "abstract": "We show that the complexity function $p_k(n)$ of a piecewise translation map conjugated to a minimal translation on the torus $\\TT^k = \\RR^k / \\ZZ^k$ is at least $kn+1$ for every integer $n$.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-02-17T06:24:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complexity function",
      "minoration",
      "minimal translation",
      "piecewise translation map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.2984B"
    }
  }
}