The best known examples of Vassiliev invariants are the coefficients of a Jones-type polynomial expanded after exponential substitution. We show that for a given knot, the first N Vassiliev invariants in this family determine the rest for some integer N.
Journal of Knot Theory and Its Ramifications
Kauffman, Louis H.; Saito, Masahico; and Sawin, Stephen F., "On finiteness of certain Vassiliev invariants" (1997). Math & Computer Science Faculty Publications. 19.
Kauffman, Louis H., Masahico Saito, and Stephen Sawin. 1997. On finiteness of certain Vassiliev invariants. Journal of Knot Theory and Its Ramifications 6 (2), 291-297.