Generic combinatorial rigidity of periodic frameworks

Justin Malestein, Louis Theran— 2013

- Focus Area 1: High-complexity Geometry - 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.

TitelGeneric combinatorial rigidity of periodic frameworks
VerfasserJustin Malestein, Louis Theran
Erschienen inAdvances in Mathematics, 233(1), 291–331, 2013.