Frameworks with forced symmetry I: Reflections and rotations
Metric Geometry
2015-03-17 v2 Combinatorics
Abstract
We give a combinatorial characterization of generic frameworks that are minimally rigid under the additional constraint of maintaining symmetry with respect to a finite order rotation or a reflection. To establish these results we develop a new technique for deriving linear representations of sparsity matroids on colored graphs and extend the direction network method of proving rigidity characterizations to handle reflections.
Keywords
Cite
@article{arxiv.1304.0398,
title = {Frameworks with forced symmetry I: Reflections and rotations},
author = {Justin Malestein and Louis Theran},
journal= {arXiv preprint arXiv:1304.0398},
year = {2015}
}
Comments
27 pages, 5 figures. All the results in this paper have appeared previously in our other papers available at arXiv:1108.2518 and arXiv:1203.2276 (v2, added some examples, discussion of non-free actions and expanded references)