ABSTRACT
The Vassiliev knot invariants were first proposed around 1989 by Victor A. A bit later, Mikhail N. Goussarov independently found a combinatorial description of the same invariants. The analogous theory can be constructed straightforwardly for the case of links; the definitions are, however, a bit more complicated. Chord diagrams are considered up to natural graph isomorphism taking chords to chords, circle to the circle and preserving the orientation of the circle. In the authors give a criterion to detect whether the derivatives of knot polynomials are Vassiliev invariants. They also show how to construct a polynomial invariant by a given Vassiliev invariant. Although other polynomials cannot be obtained from the Conway polynomial by means of a variable change, Vassiliev invariants are stronger than any of those polynomial invariants of knots.
