Abstract
AbstractIt is known that the Brandt–Lickorish–Millett–Ho polynomialQcontains Casson's knot invariant. Whether there are (essentially) other Vassiliev knot invariants obtainable fromQis an open problem. We show that this is not so up to degree 9. We also give the (apparently) first examples of knots not distinguished by 2-cable HOMFLY polynomials which are not mutants. Our calculations provide evidence of a negative answer to the question whether Vassiliev knot invariants of degreed≤ 10 are determined by the HOMFLY and Kauffman polynomials and their 2-cables, and for the existence of algebras of such Vassiliev invariants not isomorphic to the algebras of their weight systems.
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