The skein index for link invariants (Q945887)

The author introduces the skein index of a link invariant \(f\) as the mininmum \(n\) such that for any \(n+1\) tangles \(T_1, \dots, T_{n+1}\) there exist nontrivial coefficients \((a_1,\dots, a_{n+1}) \neq (0,\dots,0)\) and \(a_1f(T_1)+\cdots +a_{n+1}f(T_{n+1})=0\). It is used to compare link invariants and to find a skein relation. The author gives the complete list for the link invariants of skein index less than or equal to two, constructs a new skein relation and gives a formula for the invariant of a closed 2-braid.