Tangle Equations II

Abstract

Given two 4-plats K1 and K2. Let O be a sum of rational tangles such that N(O+P)=K1 and N(O+R)=K2, where P and R are rational tangles and N is the numerator construction on the tangles O+P and O+R, respectively. An algorithm is presented here to solve such a system of equations for O, P and R in the case where O is non rational. If two additional equations of the form N(O+R+R)=K3 and N(O+R+R+R+) =K4 are given and one of the Ki is chiral, then there is at most one solution for O and R. If all Ki are achiral then there is at most one solution together with its mirror image.