Using the HOMFLY-PT polynomial to compute knot types

Abstract

The HOMFLY-PT polynomial is a link invariant which is effective in determining chiral knot and link types with small crossing numbers. In this chapter, we concentrate on knots. We provide a guide for computing the knot types of configurations from 3D coordinates via the HOMFLY-PT polynomial using publicly-available Linux freeware. We include data on the efficacy of HOMFLY-PT for knot types through crossing number 16.