Periodic Rigidity on a Variable Torus Using Inductive Constructions

Anthony Nixon, Elissa Ross

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.

Keywords


periodic framework, generic rigidity, Henneberg operation

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