{
  "id": "1705.10291",
  "version": "v1",
  "published": "2017-05-29T17:09:27.000Z",
  "updated": "2017-05-29T17:09:27.000Z",
  "title": "A Tabulation of Ribbon Knots in Tangle Form",
  "authors": [
    "Andrey Boris Khesin"
  ],
  "comment": "10 pages, see page 9 for tangle diagrams, see page 10 for tangle information, and see page 7 for link to the table contents",
  "categories": [
    "math.GT"
  ],
  "abstract": "It is known that there are 21 ribbon knots with 10 crossings or fewer. We show that for every ribbon knot, there exists a tangle that satisfies two properties associated with the knot. First, under a specific closure, the closed tangle is equivalent to its corresponding knot. Second, under a different closure, the closed tangle is equivalent to the unlink. For each of the first 21 ribbon knots, we present a 4-strand tangle that satisfies these properties. We provide diagrams of these tangles and also express them in planar diagram notation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-29T17:09:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ribbon knot",
      "tangle form",
      "tabulation",
      "planar diagram notation",
      "closed tangle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}