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Discrete & Computational Geometry

, Volume 54, Issue 2, pp 339–367 | Cite as

Frameworks with Forced Symmetry I: Reflections and Rotations

  • Justin Malestein
  • Louis Theran
Article

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

Combinatorial rigidity Matroids Forced symmetry Colored graph 

Notes

Acknowledgments

LT was supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 247029-SDModels. JM was supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 226135. LT and JM had been supported by NSF CDI-I Grant DMR 0835586 to Igor Rivin and M. M. J. Treacy.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Mathematisches Institut der Universität BonnBonnGermany
  2. 2.Aalto Science Institute and Department of Computer ScienceAalto UniversityEspooFinland

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