{
  "id": "1106.2723",
  "version": "v1",
  "published": "2011-06-13T14:50:36.000Z",
  "updated": "2011-06-13T14:50:36.000Z",
  "title": "Prime knots whose arc index is smaller than the crossing number",
  "authors": [
    "Gyo Taek Jin",
    "Hwa Jeong Lee"
  ],
  "comment": "30 pages, 31 figures, 1 table and 379 minimal grid diagrams",
  "categories": [
    "math.GT"
  ],
  "abstract": "It is known that the arc index of alternating knots is the minimal crossing number plus two and the arc index of prime nonalternating knots is less than or equal to the minimal crossing number. We study some cases when the arc index is strictly less than the minimal crossing number. We also give minimal grid diagrams of some prime nonalternating knots with 13 crossings and 14 crossings whose arc index is the minimal crossing number minus one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-13T14:50:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "arc index",
      "prime knots",
      "prime nonalternating knots",
      "minimal crossing number plus",
      "minimal crossing number minus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.2723J"
    }
  }
}