{
  "id": "1703.04063",
  "version": "v1",
  "published": "2017-03-12T03:04:05.000Z",
  "updated": "2017-03-12T03:04:05.000Z",
  "title": "On the $k$-abelian complexity of the Cantor sequence",
  "authors": [
    "Jin Chen",
    "Xiaotao Lü",
    "Wen Wu"
  ],
  "comment": "13 pages, 3 figures",
  "categories": [
    "math.CO",
    "cs.FL",
    "math.NT"
  ],
  "abstract": "In this paper, we prove that for every integer $k \\geq 1$, the $k$-abelian complexity function of the Cantor sequence $\\mathbf{c} = 101000101\\cdots$ is a $3$-regular sequence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-12T03:04:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68R15",
      "11B85"
    ],
    "keywords": [
      "cantor sequence",
      "abelian complexity function",
      "regular sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}