Link invariants from finite Coxeter racks

TL;DR

This paper investigates Coxeter racks over finite rings and their ability to define knot and link invariants, demonstrating that enhanced invariants derived from these racks outperform traditional counting invariants.

Contribution

It introduces a novel approach to enhance rack counting invariants using the module structure of Coxeter racks over inite rings, showing increased effectiveness.

Findings

Enhanced invariants are stronger than unenhanced ones.

Module structure improves the discriminative power of knot invariants.

Examples demonstrate the effectiveness of the new invariants.

Abstract

We study Coxeter racks over $\mathbb{Z}_n$ and the knot and link invariants they define. We exploit the module structure of these racks to enhance the rack counting invariants and give examples showing that these enhanced invariants are stronger than the unenhanced rack counting invariants.