{
  "id": "2006.14534",
  "version": "v1",
  "published": "2020-06-25T16:31:09.000Z",
  "updated": "2020-06-25T16:31:09.000Z",
  "title": "A new proof of the growth rate of the solvable Baumslag-Solitar groups",
  "authors": [
    "Jennifer Taback",
    "Alden Walker"
  ],
  "comment": "18 pages, 6 figures",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "We exhibit a regular language of geodesics for a large set of elements of $BS(1,n)$ and show that the growth rate of this language is the growth rate of the group. This provides a straightforward calculation of the growth rate of $BS(1,n)$, which was initially computed by Collins, Edjvet and Gill in [5]. Our methods are based on those we develop in [8] to show that $BS(1,n)$ has a positive density of elements of positive, negative and zero conjugation curvature, as introduced by Bar-Natan, Duchin and Kropholler in [1].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-25T16:31:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F10",
      "26A12"
    ],
    "keywords": [
      "growth rate",
      "solvable baumslag-solitar groups",
      "zero conjugation curvature",
      "large set",
      "regular language"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}