• Corpus ID: 233025099

# Universal rigidity on the line, point order

```@inproceedings{Chen2021UniversalRO,
title={Universal rigidity on the line, point order},
author={Bryan Gin-ge Chen and Robert Connelly and Anthony Nixon and Louis Theran},
year={2021}
}```
• Published 5 April 2021
• Mathematics
We show that universal rigidity of a generic bar-joint framework (G,p) in R1 depends on more than the ordering of the vertices. In particular, we construct examples of 1-dimensional generic frameworks with the same graph and ordering of the vertices, such that one is universally rigid and one is not. This answers, in the negative, a question of Jordán and Nguyen. Underlying our examples are insights about how universal rigidity behaves under projections. Using these ideas, we also give a simple…

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