{
  "id": "1706.04770",
  "version": "v1",
  "published": "2017-06-15T08:14:24.000Z",
  "updated": "2017-06-15T08:14:24.000Z",
  "title": "An independence system as knot invariant",
  "authors": [
    "Usman Ali",
    "Iffat Fida Hussain"
  ],
  "comment": "17 pages,19 figures",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "An independence system (with respect to the unknotting number) is defined for a classical knot diagram. It is proved that the independence system is a knot invariant for alternating knots. The exchange property for minimal unknotting sets are also discussed. It is shown that there exists an infinite family of knot diagrams whose corresponding independence systems are matroids. In contrast, infinite families of knot diagrams exist whose independence systems are not matroids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-15T08:14:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27",
      "05B35"
    ],
    "keywords": [
      "knot invariant",
      "classical knot diagram",
      "exchange property",
      "minimal unknotting sets",
      "infinite family"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}