Using the HOMFLY-PT polynomial to compute knot types

2023/11/01 by Eric J. Rawdon, Rawdon, Eric J., Robert G. Scharein +1 · 1 citation
Mathematics · #57K10 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2311.00817

openalex publication_date 2023/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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