{
  "id": "2112.10902",
  "version": "v1",
  "published": "2021-12-20T23:05:16.000Z",
  "updated": "2021-12-20T23:05:16.000Z",
  "title": "All Prime Knots Through 10 Crossings Have Superbridge Index $\\leq 5$",
  "authors": [
    "Clayton Shonkwiler"
  ],
  "comment": "13 pages, 1 figure, 3 appendices",
  "journal": "Journal of Knot Theory and Its Ramifications 31 (2022), no. 4, 2250023",
  "doi": "10.1142/S0218216522500237",
  "categories": [
    "math.GT"
  ],
  "abstract": "This paper gives new upper bounds on the stick numbers of the knots $9_{18}$, $10_{18}$, $10_{58}$, $10_{66}$, $10_{68}$, $10_{80}$, $10_{82}$, $10_{84}$, $10_{93}$, $10_{100}$, and $10_{152}$, as well as on the equilateral stick number of $10_{79}$. These bounds imply that the knots $10_{58}$, $10_{66}$, and $10_{80}$ have superbridge index $\\leq 5$, completing the project of showing that no prime knots through 10 crossings can have superbridge index larger than 5. The current best bounds on stick number and superbridge index for prime knots through 10 crossings are given in Appendix A.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-12-20T23:05:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10",
      "53A04"
    ],
    "keywords": [
      "prime knots",
      "current best bounds",
      "equilateral stick number",
      "superbridge index larger",
      "upper bounds"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "World Scientific"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}