Andrea Alba | Searcharxiv

arXiv2026

Deciding if a shadow resolves into a given link: linear-time algorithms

A {\em shadow} (or {\em projection}) is obtained from a link diagram by ignoring the over/under information at each crossing. Given a fixed link $L$ we investigate the complexity of deciding whether an input shadow $S$ can be {\em resolved} into $L$, that is, whether we can assign over/under information to its crossings to obtain a diagram of a link isotopic to $L$. We show that if $L\in\{3_1,4_1,5_1,5_2,6_2,L2a1, L4a1, L5a1, L6n1\}$ then there exists a linear-time algorithm that decides whether an input shadow $S$ resolves into $L$.

math.GT↗

arXiv2022

Regular projections of the link L6n1

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 $L6n1$.

math.GT↗