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dc.contributor.authorGortler, Steven
dc.contributor.authorTheran, Louis
dc.contributor.authorThurston, Dylan
dc.identifier.citationGortler , S , Theran , L & Thurston , D 2019 , ' Generic unlabeled global rigidity ' , Forum of Mathematics, Sigma , vol. 7 , e21 , pp. 1-34 .
dc.identifier.otherPURE: 255207044
dc.identifier.otherPURE UUID: 040f1684-4957-4eb9-89df-d02ea731a9bb
dc.identifier.otherWOS: 000477859500001
dc.identifier.otherScopus: 85070108718
dc.identifier.otherORCID: /0000-0001-5282-4800/work/73701806
dc.descriptionThe first author was partially supported by NSF grant DMS-1564473.en
dc.description.abstractLet p be a configuration of n points in ℝd for some n and some d ≥ 2. Each pair of points has a Euclidean length in the configuration. Given some graph G on n vertices, we measure the point-pair lengths corresponding to the edges of G. In this paper, we study the question of when a generic p in d dimensions will be uniquely determined (up to an unknowable Euclidean transformation) from a given set of point-pair lengths together with knowledge of d and n. In this setting the lengths are given simply as a set of real numbers; they are not labeled with the combinatorial data that describes which point-pair gave rise to which distance, nor is data about G given. We show, perhaps surprisingly, that in terms of generic uniqueness, labels have no effect. A generic configuration is determined by an unlabeled set of point-pair distances (together with d and n) if and only if it is determined by the labeled distances.
dc.relation.ispartofForum of Mathematics, Sigmaen
dc.rightsCopyright © The Author(s) 2019. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (, which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.en
dc.subjectQA Mathematicsen
dc.titleGeneric unlabeled global rigidityen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.description.statusPeer revieweden

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