English

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.

Keywords

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

R2 v1 2026-06-21T15:59:20.092Z