Generic combinatorial rigidity of periodic frameworks

Details Generic combinatorial rigidity of periodic frameworks Generic combinatorial rigidity of periodic frameworks

2010-08-11

arxiv.org/abs/1008.1837v3

Mathematics

Combinatorics

Revised to include more figures, discussion of the one-dimensional case. 61 pages, 20 figures

Scientific paper

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 Z2-graded-sparse colored graphs.

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