{
  "id": "1501.02421",
  "version": "v1",
  "published": "2015-01-11T06:26:33.000Z",
  "updated": "2015-01-11T06:26:33.000Z",
  "title": "Minimal sufficient sets of colors and minimum number of colors",
  "authors": [
    "Jun Ge",
    "Xian'an Jin",
    "Louis H. Kauffman",
    "Pedro Lopes",
    "Lianzhu Zhang"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper we first investigate minimal sufficient sets of colors for p=11 and 13. For odd prime p and any p-colorable link L with non-zero determinant, we give alternative proofs of mincol_p L \\geq 5 for p \\geq 11 and mincol_p L \\geq 6 for p \\geq 17. We elaborate on equivalence classes of sets of distinct colors (on a given modulus) and prove that there are two such classes of five colors modulo 11, and only one such class of five colors modulo 13. Finally, we give a positive answer to a question raised by Nakamura, Nakanishi, and Satoh concerning an inequality involving crossing numbers. We show it is an equality only for the trefoil and for the figure-eight knots.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-11T06:26:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "minimal sufficient sets",
      "minimum number",
      "colors modulo",
      "figure-eight knots",
      "equivalence classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150102421G"
    }
  }
}