Periodic rigidity on a variable torus using inductive constructions

Nixon, Anthony and Ross, Elissa (2015) Periodic rigidity on a variable torus using inductive constructions. The Electronic Journal of Combinatorics, 22 (1): P1.

Preview

PDF (2212-12410-1-PB)
2212_12410_1_PB.pdf - Published Version
Download (814kB)

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.