{
  "id": "2406.04987",
  "version": "v1",
  "published": "2024-06-07T14:53:41.000Z",
  "updated": "2024-06-07T14:53:41.000Z",
  "title": "CWR sequence of invariants of alternating links and its properties",
  "authors": [
    "Michal Jablonowski"
  ],
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "We present the $CWR$ invariant, a new invariant for alternating links, which builds upon and generalizes the $WRP$ invariant. The $CWR$ invariant is an array of two-variable polynomials that provides a stronger invariant compared to the $WRP$ invariant. We compare the strength of our invariant with the classical HOMFLYPT, Kauffman $3$-variable, and Kauffman $2$-variable polynomials on specific knot examples. Additionally, we derive general recursive \"skein\" relations, and also specific formulas for the initial components of the $CWR$ invariant ($CWR_2$ and $CWR_3$) using weighted adjacency matrices of modified Tait graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-07T14:53:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "alternating links",
      "cwr sequence",
      "properties",
      "specific knot examples",
      "stronger invariant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}