On rack polynomials

TL;DR

This paper investigates rack polynomials and their associated link invariants, revealing classification results for certain racks and introducing enhanced invariants through subrack polynomials.

Contribution

It classifies constant action racks via generalized rack polynomials and introduces enhanced invariants using subrack polynomials.

Findings

Constant action racks are classified by their generalized rack polynomials.

$ns^at^a$-quandles are not classified by their generalized quandle polynomials.

Subrack polynomials lead to enhanced rack counting invariants.

Abstract

We study rack polynomials and the link invariants they define. We show that constant action racks are classified by their generalized rack polynomials and show that $ns^at^a$-quandles are not classified by their generalized quandle polynomials. We use subrack polynomials to define enhanced rack counting invariants, generalizing the quandle polynomial invariants.