Regular projections of the link L6n1

TL;DR

This paper investigates whether a given link projection can be realized as a projection of the specific link L6n1, extending previous results to this particular link.

Contribution

It provides a complete answer to the projection realization problem for the link L6n1, filling a gap in the classification of link projections.

Findings

Established criteria for projections of L6n1

Extended previous classification results

Solved the realization problem for L6n1

Abstract

Given a link projection $P$ and a link $L$, it is natural to ask whether it is possible that $P$ is a projection of $L$. Taniyama answered this question for the cases in which $L$ is a prime knot or link with crossing number at most five. Recently, Takimura settled the issue for the knot $6_2$. We answer this question for the case in which $L$ is the link $L6n1$.