{
  "id": "2410.17778",
  "version": "v1",
  "published": "2024-10-23T11:30:33.000Z",
  "updated": "2024-10-23T11:30:33.000Z",
  "title": "Determinant of the OU matrix of a braid diagram",
  "authors": [
    "Ayaka Shimizu",
    "Yoshiro Yaguchi"
  ],
  "comment": "16 pages, 6 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper, we define the OU matrix of a braid diagram and discuss how the OU matrix reflects the warping degree or the layeredness of the braid diagram, and show that the determinant of the OU matrix of a layered braid diagram is the product of the determinants of the layers. We also introduce invariants of positive braids which are derived from the OU matrix.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-23T11:30:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "determinant",
      "ou matrix reflects",
      "layered braid diagram",
      "warping degree",
      "layeredness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}