Coloring link diagrams and Conway-type polynomial of braids

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 B m . 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.