Symmetric isostatic frameworks with l^1 or l^\infty distance constraints

Kitson, Derek and Schulze, Bernd (2016) Symmetric isostatic frameworks with l^1 or l^\infty distance constraints. The Electronic Journal of Combinatorics, 23 (4): #P4.23. ISSN 1077-8926

Abstract

Combinatorial characterisations of minimal rigidity are obtained for symmetric 2-dimensional bar-joint frameworks with either l^1 or l^\infty distance constraints. The characterisations are expressed in terms of symmetric tree packings and the number of edges fixed by the symmetry operations. The proof uses new Henneberg-type inductive construction schemes.