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). Mathematics 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.