Biquandle Fares and Link Invariants

TL;DR

This paper introduces a novel family of link invariants based on fares in biquandle-colored diagrams, enhancing the ability to distinguish knots and links, with specific focus on 1-fares and 2-fares.

Contribution

It presents new invariants of knots and links using fares, including explicit examples and open questions for higher n-fares, advancing the biquandle-based invariant theory.

Findings

Proper enhancements shown for 1-fares and 2-fares

Examples demonstrate the effectiveness of the invariants

Open questions posed for n-fares with n > 2

Abstract

We introduce a new family of invariants of oriented classical and virtual knots and links using fares, maps from paths in biquandle-colored diagrams to an abelian coefficient group. We consider the cases of 1-fares and 2-fares, provide examples to show that the enhancements are proper and end with some open questions about the cases of n-fares for n > 2.