Periodic Rigidity on a Variable Torus Using Inductive Constructions

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 02 Jan 2015Embargo end date: 01 Apr 2012 United Kingdom Publisher:The Electronic Journal of CombinatoricsJournal:The Electronic Journal of Combinatorics, volume 22 (eissn: 1077-8926,

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Authors: Nixon, Anthony; Ross, Elissa;

doi: 10.37236/2212 , 10.48550/arxiv.1204.1349

arXiv: 1204.1349

Periodic Rigidity on a Variable Torus Using Inductive Constructions

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Abstract

In this paper we prove a recursive characterisation of generic rigidity for frameworks periodic with respect to a partially variable lattice. We follow the approach of modelling periodic frameworks as frameworks on a torus and use the language of gain graphs for the finite counterpart of a periodic graph. In this setting we employ variants of the Henneberg operations used frequently in rigidity theory.

Country

United Kingdom

Related Organizations

Lancaster University
United Kingdom
Worcester Polytechnic Institute
United States

Keywords

Henneberg operation, Metric Geometry (math.MG), periodic framework, 004, 510, Planar graphs; geometric and topological aspects of graph theory, 52C25, Infinite graphs, Mathematics - Metric Geometry, generic rigidity, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)

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