2023/12/26 by Yi Feng, Fengling Li, Feng, Yi +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2312.16058
openalex publication_date 2023/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 nth 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 nth polynomial.