{
  "id": "math/0506203",
  "version": "v2",
  "published": "2005-06-10T15:20:44.000Z",
  "updated": "2007-01-12T07:51:38.000Z",
  "title": "A Mealy machine with polynomial growth of irrational degree",
  "authors": [
    "Laurent Bartholdi",
    "Illya I. Reznykov"
  ],
  "comment": "20 pages, 1 diagram",
  "journal": "Internat. J. Algebra Comput. 18 (2008), no. 1, 59--82",
  "doi": "10.1142/S0218196708004287",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "We consider a very simple Mealy machine (three states over a two-symbol alphabet), and derive some properties of the semigroup it generates. In particular, this is an infinite, finitely generated semigroup; we show that the growth function of its balls behaves asymptotically like n^2.4401..., where this constant is 1 + log(2)/log((1+sqrt(5))/2); that the semigroup satisfies the identity g^6=g^4; and that its lattice of two-sided ideals is a chain.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-01-12T07:51:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M20",
      "20M35"
    ],
    "keywords": [
      "polynomial growth",
      "irrational degree",
      "two-symbol alphabet",
      "simple mealy machine",
      "growth function"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......6203B"
    }
  }
}