{
  "id": "2102.01018",
  "version": "v1",
  "published": "2021-02-01T17:48:45.000Z",
  "updated": "2021-02-01T17:48:45.000Z",
  "title": "Gaps in the Thue--Morse word",
  "authors": [
    "Lukas Spiegelhofer"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "The Thue--Morse sequence is a prototypical automatic sequence found in diverse areas of mathematics, and in computer science. We study occurrences of factors $w$ within this sequence, more precisely the sequence of gaps between consecutive occurrences. This sequence is substitutive; we prove that it is not automatic as soon as the length of $w$ is greater than $1$, thereby answering a question by J.~Shallit in the affirmative.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-01T17:48:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68Q45",
      "68R15",
      "11A63"
    ],
    "keywords": [
      "thue-morse word",
      "prototypical automatic sequence",
      "thue-morse sequence",
      "diverse areas",
      "computer science"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}