Biquandle Arrow Weight Enhacements

TL;DR

This paper introduces biquandle arrow weights, a new family of invariants for classical and virtual knots that assign weights to arrow intersections in Gauss diagrams, enhancing existing biquandle invariants.

Contribution

The paper presents a novel infinite family of biquandle enhancements called biquandle arrow weights, which are nontrivial and provide more refined knot invariants.

Findings

Enhancements are nontrivial and not determined by homset size

Applicable to both classical and virtual knots

Provide new tools for distinguishing knots

Abstract

We introduce a new infinite family of enhancements of the biquandle homset invariant called biquandle arrow weights. These invariants assign weights in an abelian group to intersections of arrows in a Gauss diagram representing a classical or virtual knot depending on the biquandle colors associated to the arrows. We provide examples to show that the enhancements are nontrivial and proper, i.e., not determined by the homset cardinality.