{
  "id": "1003.1034",
  "version": "v1",
  "published": "2010-03-04T12:56:06.000Z",
  "updated": "2010-03-04T12:56:06.000Z",
  "title": "Recurrence relation for HOMFLY polynomial and rational specializations",
  "authors": [
    "Rehana Ashraf",
    "Barbu Berceanu"
  ],
  "comment": "18 pages, 5 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Turning the skein relation for HOMFLY into a Fibonacci recurrence, we prove that there are only three rational specializations of HOMFLY polynomial: Alexander-Conway, Jones, and a new one. Using the recurrence relation, we find general and relative expansion formulae and rational generating functions for Alexander-Conway polynomial and the new polynomial, which reduce the computations to closure of simple braids, a subset of square free braids; HOMFLY polynomials of these simple braids are also computed. Algebraic independence of these three polynomials is proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-04T12:56:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57M25",
      "20F36"
    ],
    "keywords": [
      "homfly polynomial",
      "rational specializations",
      "recurrence relation",
      "simple braids",
      "square free braids"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.1034A"
    }
  }
}