Conway Polynomial

The Conway polynomial , sometimes known as the Conway-Alexander polynomial, is a modified version of the Alexander polynomial  that was formulated by J. H. Conway (Livingston 1993, pp. 207-215). It is a reparametrization of the Alexander polynomial given by

The skein relationship convention used by for the Conway polynomial is

(Doll and Hoste 1991).

Examples of Alexander  and Conway  polynomials for common knots are given in the following table

knot
trefoil knot
figure eight knot
Solomon's seal knot
stevedore's knot
Miller Institute knot

REFERENCES:

Doll, H. and Hoste, J. "A Tabulation of Oriented Links." Math. Comput. 57, 747-761, 1991.

Livingston, C. Knot Theory. Washington, DC: Math. Assoc. Amer., 1993.