$F$-polynomials of tabulated virtual knots

Abstract

A sequence of $F$-polynomials $\{F_K^n(t,\ell ){\}}_{n=1}^{\infty }$ 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.

16 pages, 8 figures, 10 tables. arXiv admin note: text overlap with arXiv:1803.05191