{
  "id": "1801.05334",
  "version": "v1",
  "published": "2018-01-16T16:12:49.000Z",
  "updated": "2018-01-16T16:12:49.000Z",
  "title": "Critical exponents of infinite balanced words",
  "authors": [
    "Narad Rampersad",
    "Jeffrey Shallit",
    "Élise Vandomme"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO",
    "cs.FL"
  ],
  "abstract": "Over an alphabet of size 3 we construct an infinite balanced word with critical exponent 2+sqrt(2)/2. Over an alphabet of size 4 we construct an infinite balanced word with critical exponent (5+sqrt(5))/4. Over larger alphabets, we give some candidates for balanced words (found computationally) having small critical exponents. We also explore a method for proving these results using the automated theorem prover Walnut.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-16T16:12:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68R15"
    ],
    "keywords": [
      "infinite balanced word",
      "automated theorem prover walnut",
      "small critical exponents",
      "larger alphabets",
      "candidates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}