{
  "id": "2203.16742",
  "version": "v1",
  "published": "2022-03-31T01:49:04.000Z",
  "updated": "2022-03-31T01:49:04.000Z",
  "title": "On the number of $k$-powers in a finite word",
  "authors": [
    "Shuo Li"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "This note is an attempt to attack a conjecture of Fraenkel and Simpson stated in 1998 concerning the number of distinct squares in a finite word. By counting the number of (right-)special factors, we give an upper bound of the number of {\\em $k$-powers} in a finite word for any integer $k\\geq 3$. By {\\em $k$-power}, we mean a word of the form $\\underbrace{uu...u}_{k \\; \\text{times}}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-31T01:49:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite word",
      "upper bound",
      "special factors",
      "distinct squares",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}