FIRST COMMON TERMS OF THE HOMFLY AND KAUFFMAN POLYNOMIALS, AND THE CONWAY POLYNOMIAL OF A KNOT

We study the first common terms of the HOMFLY and Kauffman polynomials of a knot, which we call the ϒ-polynomial, and the Conway polynomial for the 2-bridge knots and a class of 3-bridge knots. We characterize the ϒ-polynomial using the 2-bridge knots. Then we give some relations between the two polynomial invariants, and as an application, we consider the space of the Vassiliev invariant of order four.