{
  "id": "2312.16058",
  "version": "v1",
  "published": "2023-12-26T14:01:54.000Z",
  "updated": "2023-12-26T14:01:54.000Z",
  "title": "The $F$-polynomial invariant for knotoids",
  "authors": [
    "Yi Feng",
    "Fengling Li"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "As a generalization of the classical knots, knotoids deal with the open ended knot diagrams in a surface. In recent years, many polynomial invariants for knotoids have appeared, such as the bracket polynomial, the index polynomial and the $n$th polynomial, etc. In this paper, we introduce a new polynomial invariant $F$-polynomial for knotoids and discuss some properties of the $F$-polynomial. Then, we construct a family of knotoid diagrams which can be distinguished from each other by the $F$-polynomial but cannnot be distinguished by the index polynomial and the $n$th polynomial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-26T14:01:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polynomial invariant",
      "th polynomial",
      "index polynomial",
      "open ended knot diagrams",
      "knotoids deal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}