{
  "id": "math/0310144",
  "version": "v1",
  "published": "2003-10-10T10:21:16.000Z",
  "updated": "2003-10-10T10:21:16.000Z",
  "title": "A Generalization of Repetition Threshold",
  "authors": [
    "Lucian Ilie",
    "Jeffrey Shallit"
  ],
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "Brandenburg and (implicitly) Dejean introduced the concept of repetition threshold: the smallest real number alpha such that there exists an infinite word over a k-letter alphabet that avoids beta-powers for all beta>alpha. We generalize this concept to include the lengths of the avoided words. We give some conjectures supported by numerical evidence and prove one of these conjectures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-10-10T10:21:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68R15"
    ],
    "keywords": [
      "repetition threshold",
      "generalization",
      "smallest real number alpha",
      "k-letter alphabet",
      "conjectures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....10144I"
    }
  }
}