{
  "id": "2204.10204",
  "version": "v1",
  "published": "2022-04-21T15:40:24.000Z",
  "updated": "2022-04-21T15:40:24.000Z",
  "title": "On the number of squares in a finite word",
  "authors": [
    "Srečko Brlek",
    "Shuo Li"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A {\\em square} is a word of the form $uu$. In this paper we prove that for a given finite word $w$, the number of distinct square factors of $w$ is bounded by $|w|-|\\Alphabet(w)|+1$, where $|w|$ denotes the length of $w$ and $|\\Alphabet(w)|$ denotes the number of distinct letters in $w$. This result answers a conjecture of Fraenkel and Simpson stated in 1998.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-21T15:40:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68R15",
      "68R10"
    ],
    "keywords": [
      "finite word",
      "distinct square factors",
      "distinct letters",
      "result answers",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}