{
  "id": "1001.1334",
  "version": "v2",
  "published": "2010-01-08T18:50:19.000Z",
  "updated": "2011-04-09T08:01:34.000Z",
  "title": "Minimum Number of Fox Colors for Small Primes",
  "authors": [
    "P. Lopes",
    "J. Matias"
  ],
  "comment": "12 pages, 2 figures, version accepted in JKTR",
  "categories": [
    "math.GT"
  ],
  "abstract": "This article concerns exact results on the minimum number of colors of a Fox coloring over the integers modulo r, of a link with non-null determinant. Specifically, we prove that whenever the least prime divisor of the determinant of such a link and the modulus r is 2, 3, 5, or 7, then the minimum number of colors is 2, 3, 4, or 4 (respectively) and conversely. We are thus led to conjecture that for each prime p there exists a unique positive integer, m, with the following property. For any link L of non-null determinant and any modulus r such that p is the least prime divisor of the determinant of L and the modulus r, the minimum number of colors of L modulo r is m.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-04-09T08:01:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "minimum number",
      "fox colors",
      "small primes",
      "article concerns exact results",
      "non-null determinant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.1334L"
    }
  }
}