2021/11/08 by Amrendra Gill, М. А. Иванов, Gill, Amrendra +5 · 1 citation
Mathematics · #57K12 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2111.04526
openalex publication_date 2021/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
F-polynomials for virtual knots were defined by Kaur, Prabhakar and Vesnin in 2018 using flat virtual knot invariants. These polynomials naturally generalize Kauffman's affine index polynomial and use smoothing in classical crossing of a virtual knot diagram. In this paper we introduce weight functions for ordered orientable virtual and flat virtual link. A flat virtual link is an equivalence class of virtual links in respect to a local symmetry changing type of classical crossing in a diagram. By considering three types of smoothings in classical crossings of a virtual link diagram and suitable weight functions, we provide a recurrent construction for new invariants. We demonstrate by providing explicit examples, that newly defined polynomial invariants are stronger than F-polynomials.