{
  "id": "2005.03158",
  "version": "v1",
  "published": "2020-05-06T22:16:01.000Z",
  "updated": "2020-05-06T22:16:01.000Z",
  "title": "Avoiding 5/4-powers on the alphabet of nonnegative integers",
  "authors": [
    "Eric Rowland",
    "Manon Stipulanti"
  ],
  "comment": "35 pages, 3 figures",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "We identify the structure of the lexicographically least word avoiding 5/4-powers on the alphabet of nonnegative integers. Specifically, we show that this word has the form $p \\tau(\\varphi(z) \\varphi^2(z) \\cdots)$ where $p, z$ are finite words, $\\varphi$ is a 6-uniform morphism, and $\\tau$ is a coding. This description yields a recurrence for the $i$th letter, which we use to prove that the sequence of letters is 6-regular with rank 188. More generally, we prove $k$-regularity for a sequence satisfying a recurrence of the same type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-06T22:16:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68R15",
      "11B85"
    ],
    "keywords": [
      "nonnegative integers",
      "finite words",
      "description yields",
      "recurrence",
      "th letter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}