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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.22457 |
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Table of Contents:
- We establish several fundamental properties of the Rigid Unit Mode (RUM) spectrum for symmetric frameworks with a discrete abelian symmetry group and arbitrary linear constraints. In particular, we identify a nonempty subset of the RUM spectrum which derives from the joint eigenvalues of generators for the linear part of the symmetry group. These joint eigenvalues give rise to $χ$-symmetric flexes which span the space of translations for the framework. We show that the RUM spectrum is a union of Bohr-Fourier spectra arising from twisted almost-periodic flexes of the framework. We also characterise frameworks for which every almost periodic flex is a translation.