{
  "id": "1312.3710",
  "version": "v2",
  "published": "2013-12-13T05:44:24.000Z",
  "updated": "2015-02-18T15:56:43.000Z",
  "title": "An Example of an Automatic Graph of Intermediate Growth",
  "authors": [
    "Alexei Miasnikov",
    "Dmytro Savchuk"
  ],
  "comment": "16 pages, 6 figures; referee's suggestions were incorporated; to appear in Annals of Pure and Applied Logic",
  "categories": [
    "math.GR"
  ],
  "abstract": "We give an example of a 4-regular infinite automatic graph of intermediate growth. It is constructed as a Schreier graph of a certain group generated by 3-state automaton. The question was motivated by an open problem on the existence of Cayley automatic groups of intermediate growth.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-13T05:44:24.000Z",
      "abstract": "We give an example of a 4-regular infinite automatic graph of intermediate growth. It is constructed as a Schreier graph of a 2-generated self-similar group.",
      "comment": "15 pages, 6 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-02-18T15:56:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "intermediate growth",
      "cayley automatic groups",
      "infinite automatic graph",
      "open problem",
      "schreier graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.3710M"
    }
  }
}