[For the entire collection see Zbl 0747.00039.]
In his seminal paper [“An enumeration of knots and links and some of their algebraic properties”, in: Computational problems in abstract algebra, Proc. Conf. Oxford 1967, 329-358 (1970; Zbl 0202.547)], J. H. Conway introduced several identities satisfied by the potential functions of knots and links in the three-sphere. Only the first of Conway’s identities is required to determine the reduced (one-variable) potential function, but it has remained an open problem to determine whether or not some set of identities could be found that would determine the unreduced (multivariate) potential function. M. E. Kidwell [Proc. Am. Math. Soc. 98, 485-494 (1986; Zbl 0613.57001)] and Y. Nakanishi [Tokyo J. Math. 13, 163-177 (1990; Zbl 0716.57003)] have solved this problem for two- and three-variable potential functions, resp.
The author presents a general solution. The most original ingredient is a fairly complicated identity involving six links which differ locally in their arrangements of three strands.