Recurrent Generalization of F-Polynomials for Virtual Knots and Links

F-polynomials for virtual knots were defined by Kaur, Prabhakar and Vesnin in 2018 using flat knot invariants. These polynomials naturally generalize Kauffman’s affine index polynomial use smoothing the classical crossing of a diagram. In this paper, we introduce weight functions ordered orientable links. A link is an equivalence class links with respect to local symmetry changing type By considering three types crossings diagram suitable functions, there provided recurrent construction new It demonstrated explicit examples that newly invariants are stronger than F-polynomials.