Rigid frameworks with dilation constraints

Dewar, Sean and Nixon, Anthony and Sainsbury, Andrew (2025) Rigid frameworks with dilation constraints. Discrete Mathematics, 348 (2): 114304. ISSN 0012-365X

Text (DilationRigidityAuthorAccepted)
DilationRigidityAuthorAccepted.pdf - Accepted Version
Available under License Creative Commons Attribution.
Download (380kB)

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.