# 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.

Title

Generic combinatorial rigidity of periodic frameworks

Author

Justin Malestein, Louis Theran

Date

2013-01

Source(s)

Appeared in

Advances in Mathematics, 233(1), 291–331, 2013.

Type

Text