{
  "id": "1201.2109",
  "version": "v1",
  "published": "2012-01-10T16:52:25.000Z",
  "updated": "2012-01-10T16:52:25.000Z",
  "title": "Abelian complexity and Abelian co-decomposition",
  "authors": [
    "Ondřej Turek"
  ],
  "comment": "23 pages",
  "journal": "Theor. Comput. Sci. 469 (2013), 77-91",
  "doi": "10.1016/j.tcs.2012.10.034",
  "categories": [
    "math.CO"
  ],
  "abstract": "We propose a technique for exploring the abelian complexity of recurrent infinite words, focusing particularly on infinite words associated with Parry numbers. Using that technique, we give the affirmative answer to the open question posed by Richomme, Saari and Zamboni, whether the abelian complexity of the Tribonacci word attains each value in $\\{4,5,6\\}$ infinitely many times.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-01-10T16:52:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68R15"
    ],
    "keywords": [
      "abelian complexity",
      "abelian co-decomposition",
      "recurrent infinite words",
      "tribonacci word attains",
      "parry numbers"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.2109T"
    }
  }
}