A note on Vassiliev invariants not contained in the knot polynomials (Q2720950)

Briefly after the introduction of the Vassiliev knot invariants it was discovered that a lot of such invariants can be obtained from knot polynomials. In particular, the number of Vassiliev invariants of a given degree arising from the HOMFLY and Kauffman polynomials was computed. The purpose of this note is to collect some examples showing that some Vassiliev invariants are not obtainable from the HOMFLY and Kauffman polynomials and distinguish knots which cannot be distinguished by HOMFLY and/or Kauffman polynomials. The constructed examples are of degree 5, 6 and 7. It is known that all Vassiliev invariants of degree at most 4 and two of the three primitive Vassiliev invariants of degree 5 can be obtained from the HOMFLY polynomial; all invariants of degree \(\leq 5\) and four of the five primitive invariants of degree 6 can be obtained from the Kauffman polynomial.