$F$-polynomials of tabulated virtual knots

Maxim Ivanov; Andrei Vesnin

doi:10.1142/s0218216520500546

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arXiv · 1906.01976

$F$-polynomials of tabulated virtual knots

Maxim Ivanov·Andrei Vesnin

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Abstract

A sequence of $F$-polynomials $\{ F^n_K (t, \ell)\}_{n=1}^{\infty}$ of virtual knots $K$ was defined by Kaur, Prabhakar, and Vesnin in 2018. These polynomials have been expressed in terms of index value of crossing and $n$-writhe of $K$. By the construction, $F$-polynomials are generalizations of the Kauffman's Affine Index Polynomial, and are invariants of virtual knot $K$. We present values of $F$-polynomials of oriented virtual knots having at most four classical crossings in a diagram.

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Maxim Ivanov, Andrei Vesnin. 2019-06-02. $F$-polynomials of tabulated virtual knots. https://doi.org/10.1142/s0218216520500546

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