Полиномы простых виртуальных узлов рода один и сложности не более пяти

Translated title of the contribution: The polynomials of prime virtual knots of genus 1 and complexity at most 5

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Abstract

Akimova and Matveev classified the prime virtual knots of genus 1 which admit diagrams with at most 5 classical crossings in 2017. In 2018, Kaur, Prabhakar, and Vesnin introduced the families of the L- and F-polynomials of virtual knots generalizing the Kauffman affine index polynomial. We introduce the notion of a totally flat-trivial virtual knot. We prove that the L- and F-polynomials for these knots coincide with the affine index polynomial. Also, we establish that all Akimova–Matveev knots are totally flat-trivial and calculate their affine index polynomials.
Translated title of the contributionThe polynomials of prime virtual knots of genus 1 and complexity at most 5
Original languageRussian
Article number4
Pages (from-to)1247-1256
Number of pages10
JournalСибирский математический журнал
Volume61
Issue number6
DOIs
Publication statusPublished - 2020

OECD FOS+WOS

  • 1.01 MATHEMATICS

State classification of scientific and technological information

  • 27.19 Topology

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