Generalized quandle polynomials

TL;DR

This paper introduces a new family of eight-variable polynomial invariants for finite biquandles, extending previous quandle polynomials and link invariants to provide more comprehensive tools for knot theory analysis.

Contribution

It presents a natural generalization of the two-variable quandle polynomial to eight-variable invariants for finite biquandles, enhancing the capability to distinguish links.

Findings

Eight-variable polynomial invariants for finite biquandles introduced

These invariants generalize the quandle counting invariant

New tools for analyzing link properties in knot theory

Abstract

We define a family of generalizations of the two-variable quandle polynomial. These polynomial invariants generalize in a natural way to eight-variable polynomial invariants of finite biquandles. We use these polynomials to define a family of link invariants which further generalize the quandle counting invariant.