HOMFLY Polynomials of Some Generalized Hopf Links

The Hopf link, consisting of two unknots wrapped around each other, is the simplest possible nontrivial link with more than one component. We can generalize it to two bundles of "parallel" unknots wrapped around each other. In this paper, we show that when one of the two bundles has a fixed side, the HOMFLY polynomials of the links satisfy a system of recurrence equations. This leads to a procedure for computing explicit formulas for the HOMFLY polynomials.