{
  "id": "1007.3278",
  "version": "v2",
  "published": "2010-07-19T20:43:25.000Z",
  "updated": "2011-01-20T23:14:26.000Z",
  "title": "Upper bounds in the Ohtsuki-Riley-Sakuma partial order on 2-bridge knots",
  "authors": [
    "Scott M. Garrabrant",
    "Jim Hoste",
    "Patrick D. Shanahan"
  ],
  "comment": "21 pages, 2 figures. This is a significant revision of the paper \"Two-bridge knots with common ORS covers,\" including a proof of Conjecture 1. We have retitled the paper and added an author",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper we use continued fractions to study a partial order on the set of 2-bridge knots derived from the work of Ohtsuki, Riley, and Sakuma. We establish necessary and sufficient conditions for any set of 2-bridge knots to have an upper bound with respect to the partial order. Moreover, given any 2-bridge knot K we characterize all other 2-bridge knots J such that {K, J} has an upper bound. As an application we answer a question of Suzuki, showing that there is no upper bound for the set consisting of the trefoil and figure-eight knots.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-01-20T23:14:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "upper bound",
      "ohtsuki-riley-sakuma partial order",
      "figure-eight knots",
      "sufficient conditions",
      "continued fractions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.3278G"
    }
  }
}