Vassiliev knot invariants derived from cable Γ-polynomials

摘要

For coprime integers p(0) and q, the (p, q)-cable Gamma-polynomial of a knot K is the Gamma-polynomial of the (p, q)-cable knot of K, where the Gamma-polynomial is the common zeroth coefficient polynomial of the HOMFLYPT and Kauffman polynomials. In this paper, we give some results on Vassiliev knot invariants derived from the cable Gamma-polynomials. In particular, we show that all Vassiliev knot invariants of order = 4 are determined by the cable Gamma-polynomials. (C) 2020 Elsevier B.V. All rights reserved.