Single-Boundary Iteration for Polynomial Invariants

Abstract

In an earlier paper [1] we show that if a family of oriented links obey an iterative pattern, their HOMFLY polynomials satisfy a homogeneous linear recurrence relation. This also holds for Kauffman polynomials. Here we prove the result using a different construction which in some cases yields a recurrence relation of much lower order, thereby drastically reducing the amount of computation required to obtain explicit polynomials for individual members or a general formula for the entire family.