{
  "id": "1309.4184",
  "version": "v3",
  "published": "2013-09-17T05:07:42.000Z",
  "updated": "2013-12-20T06:43:37.000Z",
  "title": "The cogrowth series for $\\mathrm{BS}(N,N)$ is D-finite",
  "authors": [
    "M. Elder",
    "A. Rechnitzer",
    "E. J. Janse van Rensburg",
    "T. Wong"
  ],
  "comment": "16 pages, 1 figure, 1 table. This article supersedes arXiv:1210.3425",
  "journal": "International Journal of Algebra and Computation 24 (2014) Issue 2 pages 171-187",
  "doi": "10.1142/S0218196714500106",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "We compute the cogrowth series for Baumslag-Solitar groups $\\mathrm{BS}(N,N) = < a,b | a^N b = b a^N > $, which we show to be D-finite. It follows that their cogrowth rates are algebraic numbers.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-12-20T06:43:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F69",
      "20F65",
      "05A15"
    ],
    "keywords": [
      "cogrowth series",
      "baumslag-solitar groups",
      "cogrowth rates"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.4184E"
    }
  }
}