{
  "id": "0809.1334",
  "version": "v4",
  "published": "2008-09-08T14:09:34.000Z",
  "updated": "2009-06-02T07:03:18.000Z",
  "title": "The warping degree of a knot diagram",
  "authors": [
    "Ayaka Shimizu"
  ],
  "comment": "12 pages, 9 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "For an oriented knot diagram D, the warping degree d(D) is the smallest number of crossing changes which are needed to obtain the monotone diagram from D in the usual way. We show that d(D) + d(-D) + 1 is less than or equal to the crossing number of D. Moreover the equality holds if and only if D is an alternating diagram.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-06-02T07:03:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "warping degree",
      "equality holds",
      "oriented knot diagram",
      "monotone diagram",
      "usual way"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.1334S"
    }
  }
}