Generalized Quandle Polynomials and Their Applications to Stuquandles, Stuck Links, and RNA Folding

TL;DR

This paper introduces a generalized quandle polynomial invariant applicable to stuquandles, stuck links, and RNA folding, providing new tools for analyzing complex topological and biological structures.

Contribution

It presents a novel generalized quandle polynomial invariant and demonstrates its applications to stuquandles, stuck links, and RNA folding structures.

Findings

Polynomial invariant of stuquandles established

Invariant applied to stuck links and RNA foldings

Explicit computations demonstrate the invariant's effectiveness

Abstract

We introduce a generalization of the quandle polynomial. We prove that our polynomial is an invariant of stuquandles. Furthermore, we use the invariant of stuquandles to define a polynomial invariant of stuck links. As a byproduct, we obtain a polynomial invariant of RNA foldings. Lastly, we provide explicit computations of our polynomial invariant for both stuck links and RNA foldings.