Pointed Quandle Coloring Quivers of Linkoids

TL;DR

This paper introduces new quiver-based invariants for linkoids, generalizing existing link invariants and providing tools for their analysis, especially for torus-type linkoids with dihedral quandles.

Contribution

It develops pointed quandle coloring quivers for linkoids, generalizes the in-degree polynomial invariant, and introduces the in-degree quiver polynomial matrix.

Findings

Generalized in-degree polynomial to linkoids

Defined the in-degree quiver polynomial matrix

Analyzed linkoids of (p,2)-torus type with dihedral quandles

Abstract

We enhance the pointed quandle counting invariant of linkoids through the use of quivers analogously to quandle coloring quivers. This allows us to generalize the in-degree polynomial invariant of links to linkoids. Additionally, we introduce a new linkoid invariant, which we call the in-degree quiver polynomial matrix. Lastly, we study the pointed quandle coloring quivers of linkoids of $(p,2)$-torus type with respect to pointed dihedral quandles.