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Rigid frameworks with dilation constraints

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published
Article number114304
<mark>Journal publication date</mark>28/02/2025
<mark>Journal</mark>Discrete Mathematics
Issue number2
Volume348
Publication StatusPublished
Early online date31/10/24
<mark>Original language</mark>English

Abstract

We consider the rigidity and global rigidity of bar-joint frameworks in Euclidean d-space under additional dilation constraints in specified coordinate directions. In this setting we obtain a complete characterisation of generic rigidity. We then consider generic global rigidity. In particular, we provide an algebraic sufficient condition and a weak necessary condition. We also construct a large family of globally rigid frameworks and conjecture a combinatorial characterisation when most coordinate directions have dilation constraints.