Topological designs

Justin Malestein, Louis Theran— 2014

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.

TitleTopological designs
AuthorJustin Malestein, Louis Theran
Size or Duration60 pages