{
  "id": "2108.00563",
  "version": "v1",
  "published": "2021-08-01T23:37:47.000Z",
  "updated": "2021-08-01T23:37:47.000Z",
  "title": "A lower bound on the average genus of a 2-bridge knot",
  "authors": [
    "Moshe Cohen"
  ],
  "comment": "17 pages, 6 figures, 4 tables",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "Experimental data from Dunfield et al using random grid diagrams suggests that the genus of a knot grows linearly with respect to the crossing number. Using billiard table diagrams of Chebyshev knots developed by Koseleff and Pecker and a random model of 2-bridge knots via these diagrams developed by the author with Krishnan and then with Even-Zohar and Krishnan, we introduce a further-truncated model of all 2-bridge knots of a given crossing number, almost all counted twice. We present a convenient way to count Seifert circles in this model and use this to compute a lower bound for the average Seifert genus of a 2-bridge knot of a given crossing number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-01T23:37:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10",
      "05A05"
    ],
    "keywords": [
      "lower bound",
      "average genus",
      "crossing number",
      "count seifert circles",
      "average seifert genus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}