Generic combinatorial rigidity of periodic frameworks

@article{Malestein2013GenericCR,
  title={Generic combinatorial rigidity of periodic frameworks},
  author={Justin Malestein and Louis Theran},
  journal={Advances in Mathematics},
  year={2013},
  volume={233},
  pages={291-331}
}
Abstract We give a combinatorial characterization of generic minimal rigidity for planar periodic frameworks . The characterization is a true analogue of the Maxwell–Laman Theorem from rigidity theory: it is stated in terms of a finite combinatorial object and the conditions are checkable by polynomial time combinatorial algorithms. To prove our rigidity theorem we introduce and develop periodic direction networks and Z 2 - graded-sparse colored graphs . 
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