Generic combinatorial rigidity of periodic frameworks
Combinatorics
2012-10-24 v4 Geometric Topology
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 Z2-graded-sparse colored graphs.
Cite
@article{arxiv.1008.1837,
title = {Generic combinatorial rigidity of periodic frameworks},
author = {Justin Malestein and Louis Theran},
journal= {arXiv preprint arXiv:1008.1837},
year = {2012}
}
Comments
Some typographical errors fixed. 61 pages, to appear in Advances in Math