{
  "id": "1910.09190",
  "version": "v1",
  "published": "2019-10-21T07:48:23.000Z",
  "updated": "2019-10-21T07:48:23.000Z",
  "title": "Identities of the Kauffman Monoid $\\mathcal{K}_4$ and of the Jones monoid $\\mathcal{J}_4$",
  "authors": [
    "N. V. Kitov",
    "M. V. Volkov"
  ],
  "comment": "25 pages, 7 figures",
  "categories": [
    "math.GR",
    "cs.CC"
  ],
  "abstract": "Kauffman monoids $\\mathcal{K}_n$ and Jones monoids $\\mathcal{J}_n$, $n=2,3,\\dots$, are two families of monoids relevant in knot theory. We prove a somewhat counterintuitive result that the Kauffman monoids $\\mathcal{K}_3$ and $\\mathcal{K}_4$ satisfy exactly the same identities. This leads to a polynomial time algorithm to check whether a given identity holds in $\\mathcal{K}_4$. As a byproduct, we also find a polynomial time algorithm for checking identities in the Jones monoid $\\mathcal{J}_4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-21T07:48:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M05",
      "68Q17"
    ],
    "keywords": [
      "jones monoid",
      "kauffman monoid",
      "polynomial time algorithm",
      "knot theory",
      "somewhat counterintuitive result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}