3 papers
math.GT2026
Permutation Jones Polynomials
Sam Nelson
We introduce a generalization of the Jones polynomial for classical and virtual knots and links using colorings by a permutation of a finite set . For and…
math.GT2026
Biquandle Arrow Weight Quiver Representations
Sam Nelson, Migiwa Sakurai
We define an infinite family of quiver representation-valued invariants of classical and virtual knots associated to a choice of data vector consisting of a biquandle, abelian grou…
math.GT2026
A Survey of Quantum Enhancements
Sam Nelson
In this short survey article we collect the current state of the art in the nascent field of \textit{quantum enhancements}, a type of knot invariant defined by collecting values of…