TY - JOUR

T1 - Recurrent generalization of f-polynomials for virtual knots and links

AU - Gill, Amrendra

AU - Ivanov, Maxim

AU - Prabhakar, Madeti

AU - Vesnin, Andrei

N1 - Funding Information: Author Contributions: Investigation, A.G., M.I., M.P. and A.V.; Methodology, A.G., M.I., M.P. and A.V.; Writing—original draft, A.G., M.I., M.P. and A.V.; Writing—review and editing, A.G., M.I., M.P. and A.V. The authors contributed equally to this work. All authors have read and agreed to the published version of the manuscript Funding: A.G. and M.P. were supported by DST (project number DST/INT/RUS/RSF/P-02), M.I. was supported by RFBR (grant number 19-01-00569), and A.V. was supported by RSF (grant number 20-61-46005). Publisher Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2022/1

Y1 - 2022/1

N2 - 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 the classical crossing of a virtual knot diagram. In this paper, we introduce weight functions for ordered orientable virtual and flat virtual links. A flat virtual link is an equivalence class of virtual links with respect to a local symmetry changing a type of classical crossing in a diagram. By considering three types of smoothing in classical crossings of a virtual link diagram and suitable weight functions, there is provided a recurrent construction for new invariants. It is demonstrated by explicit examples that newly defined polynomial invariants are stronger than F-polynomials.

AB - 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 the classical crossing of a virtual knot diagram. In this paper, we introduce weight functions for ordered orientable virtual and flat virtual links. A flat virtual link is an equivalence class of virtual links with respect to a local symmetry changing a type of classical crossing in a diagram. By considering three types of smoothing in classical crossings of a virtual link diagram and suitable weight functions, there is provided a recurrent construction for new invariants. It is demonstrated by explicit examples that newly defined polynomial invariants are stronger than F-polynomials.

KW - Difference writhe

KW - Flat virtual knot invariant

KW - Virtual knot invariant

UR - http://www.scopus.com/inward/record.url?scp=85121811431&partnerID=8YFLogxK

U2 - 10.3390/sym14010015

DO - 10.3390/sym14010015

M3 - Article

AN - SCOPUS:85121811431

VL - 14

JO - Symmetry

JF - Symmetry

SN - 2073-8994

IS - 1

M1 - 15

ER -