{
  "id": "1406.1587",
  "version": "v1",
  "published": "2014-06-06T05:39:19.000Z",
  "updated": "2014-06-06T05:39:19.000Z",
  "title": "A combinatorial proof of the non-vanishing of Hankel determinants of the Thue--Morse sequence",
  "authors": [
    "Yann Bugeaud",
    "Guo-Niu Han"
  ],
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "In 1998, Allouche, Peyri\\`ere, Wen and Wen established that the Hankel determinants associated with the Thue--Morse sequence on $\\{-1, 1\\}$ are always nonzero. Their proof depends on a set of sixteen recurrence relations. We present an alternative, purely combinatorial proof of the same result. We also re-prove a recent result of Coons on the non-vanishing of the Hankel determinants associated to two other classical integer sequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-06T05:39:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "11J82"
    ],
    "keywords": [
      "thue-morse sequence",
      "hankel determinants",
      "non-vanishing",
      "proof depends",
      "classical integer sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.1587B"
    }
  }
}