English

The $F$-polynomial invariant for knotoids

Geometric Topology 2023-12-27 v1

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 nnth polynomial, etc. In this paper, we introduce a new polynomial invariant FF-polynomial for knotoids and discuss some properties of the FF-polynomial. Then, we construct a family of knotoid diagrams which can be distinguished from each other by the FF-polynomial but cannnot be distinguished by the index polynomial and the nnth polynomial.

Keywords

Cite

@article{arxiv.2312.16058,
  title  = {The $F$-polynomial invariant for knotoids},
  author = {Yi Feng and Fengling Li},
  journal= {arXiv preprint arXiv:2312.16058},
  year   = {2023}
}
R2 v1 2026-06-28T14:02:09.925Z