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

Andrea Alba, Gelasio Salazar

math.GTarXiv:2608.19484

Abstract

A shadow (or 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 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∈\31,41,51,52,62,L2a1, L4a1, L5a1, L6n1\ then there exists a linear-time algorithm that decides whether an input shadow S resolves into L.

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