Prime knots with arc index 12 up to 16 crossings

Abstract

Every tame link admits an embedding into a finite union of half-planes emanating from a common straight line, so that each half-plane intersects the link in a simple arc. The minimal number of half-planes required for such an embedding is called the arc index of the link. Here we present the list of all prime knots up to 16 crossings which have arc index 12, together with their minimal arc presentations. Upon doing the classification, we also discuss how to decide whether a given arc presentation of a knot can be transformed to another with fewer half-planes.