English

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)

R2 v1 2026-06-21T23:51:38.168Z