An example of semiquandle and u-polynomials for flat virtual knots via this semiquandle coloring

TL;DR

This paper introduces a new semiquandle-based invariant for flat virtual knots and explores its relation to u-polynomials, providing new tools for analyzing these complex link structures.

Contribution

It presents specific examples of semiquandles and demonstrates their use in defining invariants for flat virtual knots, linking them to u-polynomials.

Findings

Semiquandle examples for flat virtual knots are provided.

A new invariant based on semiquandle coloring is introduced.

The relation between the invariant and u-polynomials is established.

Abstract

Flat virtual links are some variant of links, and semiquandles are counterparts of quandles or biquandles, which axiomize the Reidemeister-like moves. In this paper, we give some example of semiquandle and introduce an invariant for flat virtual knot using it. We also explain that it relates to the u-polynomials for flat virtual knots.