Coloring link diagrams and Conway-type polynomial of braids

Abstract

In this paper we define and present a simple combinatorial formula for a 3-variable Laurent polynomial invariant I(a, z, t) of conjugacy classes in Artin braid group Bm. We show that the Laurent polynomial I(a, z, t) satisfies the Conway skein relation and the coefficients of the 1-variable polynomial t −k I(a, z, t)|a=1,t=0 are Vassiliev invariants of braids.