30 citations · 184 across the 89 of their papers we have counts for
95 papers
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 f…
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…
Biquandle Brackets and Quivers
Sam Nelson
In this brief expository article we review the background for biquandle bracket quivers -- including biquandles, biquandle homsets, biquandle coloring quivers and biquandle bracket…
Entropic Niebrzydowski Tribrackets
Jieon Kim, Sam Nelson
We introduce the notion of entropic Niebrzydowski tribrackets or just entropic tribrackets, analogous to entropic (also known as abelian or medial ) quandles and biquandles. We sho…
Marked Graph Mosaics
Seonmi Choi, Sam Nelson
We consider the notion of mosaic diagrams for surface-links using marked graph diagrams. We establish bounds, in some cases tight, on the mosaic numbers for the surface-links with…
Biquandle Arrow Weight Enhacements
Sam Nelson, Migiwa Sakurai
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 intersec…