{
  "id": "0906.2850",
  "version": "v1",
  "published": "2009-06-16T14:29:15.000Z",
  "updated": "2009-06-16T14:29:15.000Z",
  "title": "Regular sets and counting in free groups",
  "authors": [
    "Elizaveta Frenkel",
    "Alexei G. Myasnikov",
    "Vladimir N. Remeslennikov"
  ],
  "comment": "33 pp, 5 figures",
  "categories": [
    "math.GR",
    "math.PR"
  ],
  "abstract": "In this paper we study asymptotic behavior of regular subsets in a free group F of finite rank, compare their sizes at infinity, and develop techniques to compute the probabilities of sets relative to distributions on F that come naturally from no-return random walks on the Cayley graph of F. We apply these techniques to study cosets, double cosets, and Schreier representatives of finitely generated subgroups of F and also to analyze relative sizes of regular prefixed-closed subsets in F.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-06-16T14:29:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E05"
    ],
    "keywords": [
      "free group",
      "regular sets",
      "study asymptotic behavior",
      "no-return random walks",
      "regular subsets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.2850F"
    }
  }
}