{
  "id": "1908.09663",
  "version": "v1",
  "published": "2019-08-26T13:17:12.000Z",
  "updated": "2019-08-26T13:17:12.000Z",
  "title": "Polynomials of genus one prime knots of complexity at most five",
  "authors": [
    "Maxim Ivanov",
    "Andrei Vesnin"
  ],
  "comment": "11 pages, 7 figures, 4 tables",
  "categories": [
    "math.GT"
  ],
  "abstract": "Prime knots of genus one admitting diagram with at most five classical crossings were classified by Akimova and Matveev in 2014. In 2018 Kaur, Prabhakar and Vesnin introduced families of L-polynomials and F-polynomials for virtual knots which are generalizations of affine index polynomial. Here we introduce a notion of totally flat-trivial knots and demonstrate that for such knots F-polynomials and L-polynomials coincide with affine index polynomial. We prove that all Akimova - Matveev knots are totally flat-trivial and calculate their affine index polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-26T13:17:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "prime knots",
      "affine index polynomial",
      "complexity",
      "matveev knots",
      "l-polynomials coincide"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}