{
  "id": "0811.3990",
  "version": "v1",
  "published": "2008-11-24T22:58:01.000Z",
  "updated": "2008-11-24T22:58:01.000Z",
  "title": "Phase transitions in infinitely generated groups, and related problems in additive number theory",
  "authors": [
    "Melvyn B. Nathanson"
  ],
  "comment": "11 pages",
  "journal": "Integers 11A (2011), Article 17, 1--14",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "Let A be an infinite set of generators for a group G, and let L_A(r) denote the number of elements of G whose word length with respect to A is exactly r. The purpose of this note is to determine all growth functions L_A(r) associated to infinite generating sets for groups, and to describe a phase transition phenomenon associated with infinite generating sets. A list of open problems is also.included.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-24T22:58:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "11B13",
      "11B34",
      "11B75"
    ],
    "keywords": [
      "additive number theory",
      "infinitely generated groups",
      "related problems",
      "infinite generating sets",
      "phase transition phenomenon"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.3990N"
    }
  }
}