{
  "id": "2003.10721",
  "version": "v1",
  "published": "2020-03-24T08:59:38.000Z",
  "updated": "2020-03-24T08:59:38.000Z",
  "title": "A gap of the exponents of repetitions of Sturmian words",
  "authors": [
    "Suzue Ohnaka",
    "Takao Watanabe"
  ],
  "comment": "30 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "By measuring the smallest second occuring time of every factor of an infinite word $x$, Bugeaud and Kim introduced a new quantity ${\\rm rep}(x)$ called the exponent of repetition of $x$. Among other results, Bugeaud and Kim proved that $1 \\leq {\\rm rep}(x) \\leq r_{\\max} = \\sqrt{10} - 3/2$ and $r_{\\max}$ is the isolated maximum value when $x$ varies over the Sturmian words. In this paper, we determine the value $r_1$ such that there is no Sturmian word $x$ satisfying $r_1 < {\\rm rep}(x) < r_{\\max}$ and $r_1$ is an accumulate point of the set of ${\\rm rep}(x)$ when $x$ runs over the Sturmian words.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-24T08:59:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68R15",
      "11A55",
      "11A63"
    ],
    "keywords": [
      "sturmian word",
      "repetition",
      "smallest second occuring time",
      "accumulate point",
      "infinite word"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}