{
  "id": "1204.0597",
  "version": "v3",
  "published": "2012-04-03T05:06:17.000Z",
  "updated": "2014-11-10T13:25:34.000Z",
  "title": "Arc index of pretzel knots of type $(-p,q,r)$",
  "authors": [
    "Hwa Jeong Lee",
    "Gyo Taek Jin"
  ],
  "comment": "12 pages, 7 figures, 2 tables",
  "categories": [
    "math.GT"
  ],
  "abstract": "We computed the arc index for some of the pretzel knots $K=P(-p,q,r)$ with $p,q,r\\ge2$, $r\\geq q$ and at most one of $p,q,r$ is even. If $q=2$, then the arc index $\\alpha(K)$ equals the minimal crossing number $c(K)$. If $p\\ge3$ and $q=3$, then $\\alpha(K)=c(K)-1$. If $p\\ge5$ and $q=4$, then $\\alpha(K)=c(K)-2$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-01-25T14:16:36.000Z",
      "comment": "10 pages, 7 figures, 2 tables",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-11-10T13:25:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57M25"
    ],
    "keywords": [
      "arc index",
      "pretzel knots",
      "minimal crossing number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.0597L"
    }
  }
}