{
  "id": "0808.0573",
  "version": "v2",
  "published": "2008-08-05T08:24:46.000Z",
  "updated": "2008-12-10T19:22:35.000Z",
  "title": "The dealternating number and the alternation number of a closed 3-braid",
  "authors": [
    "Tetsuya Abe",
    "Kengo Kishimoto"
  ],
  "comment": "We corrected Section 6",
  "categories": [
    "math.GT"
  ],
  "abstract": "We give an upper bound for the dealternating number of a closed 3-braid. As applications, we determine the dealternating numbers, the alternation numbers and the Turaev genera of some closed positive 3-braids. We also show that there exist infinitely many positive knots with any dealternating number (or any alternation number) and any braid index.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-12-10T19:22:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "dealternating number",
      "alternation number",
      "upper bound",
      "turaev genera"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.0573A"
    }
  }
}