{
  "id": "math/0511474",
  "version": "v1",
  "published": "2005-11-18T21:32:04.000Z",
  "updated": "2005-11-18T21:32:04.000Z",
  "title": "Growth of positive words and lower bounds of the growth rate for Thompson's groups $F(p)$",
  "authors": [
    "Jose Burillo",
    "Victor Guba"
  ],
  "comment": "17 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $F(p)$, $p\\ge2$ be the family of generalized Thompson's groups. Here F(2) is the famous Richard Thompson's group usually denoted by $F$. We find the growth rate of the monoid of positive words in $F(p)$ and show that it does not exceed $p+1/2$. Also we describe new normal forms for elements of $F(p)$ and, using these forms, we find a lower bound for the growth rate of $F(p)$ in its natural generators. This lower bound asymptotically equals $(p-1/2)\\log_2 e+1/2$ for large values of $p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-11-18T21:32:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F32",
      "05C25"
    ],
    "keywords": [
      "growth rate",
      "positive words",
      "lower bound asymptotically equals",
      "famous richard thompsons group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....11474B"
    }
  }
}