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Recurrent generalization of f-polynomials for virtual knots and links Full article

Journal Symmetry
ISSN: 2073-8994
Output data Year: 2022, Volume: 14, Number: 1, Article number : 15, Pages count : DOI: 10.3390/sym14010015
Tags Difference writhe; Flat virtual knot invariant; Virtual knot invariant
Authors Gill A. 1 , Ivanov M. 2 , Prabhakar M. 1 , Vesnin A. 3,4,5
Affiliations
1 Department of Mathematics, Indian Institute of Technology Ropar, Punjab, Rupnagar, 140001, India
2 Laboratory of Topology and Dynamics, Novosibirsk State University, Novosibirsk, 630090, Russian Federation
3 Regional Scientific and Educational Mathematical Center, Tomsk State University, Tomsk, 634050, Russian Federation
4 Faculty of Mathematics, National Research University “Higher School of Economics”, Moscow, 109028, Russian Federation
5 Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090, Russian Federation

Funding (2)

1 Russian Foundation for Basic Research 19-01-00569
2 Russian Science Foundation 20-61-46005

Abstract: 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.
Cite: Gill A. , Ivanov M. , Prabhakar M. , Vesnin A.
Recurrent generalization of f-polynomials for virtual knots and links
Symmetry. 2022. V.14. N1. 15 . DOI: 10.3390/sym14010015 WOS Scopus РИНЦ OpenAlex
Identifiers:
Web of science: WOS:000757263800001
Scopus: 2-s2.0-85121811431
Elibrary: 47546210
OpenAlex: W3211694458
Citing:
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Scopus 2
Web of science 2
OpenAlex 2
Elibrary 1
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