Taizo Kanenobu
Abstract
We give a basis for the space of the Vassiliev knot invariants of order 6, which implies a sixth order Vassiliev knot invariant is determined by its HOMFLY and Kauffman polynomials. Furthermore, we show that there is a seventh order invariant which cannot be obtained from these polynomials of a knot.
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We give a basis for the space of the Vassiliev knot invariants of order 6, which implies a sixth order Vassiliev knot invariant is determined by its HOMFLY and Kauffman polynomials. Furthermore, we show that there is a seventh order invariant which cannot be obtained from these polynomials of a knot.
Key concepts: Mathematics, Knot polynomial, Quantum invariant, Knot (papermaking), Knot invariant, Tricolorability, Skein relation, Knot theory