Symmetric Isostatic Frameworks with $\ell^1$ or $\ell^\infty$ Distance Constraints

Derek Kitson, Bernd Schulze

Abstract


Combinatorial characterisations of minimal rigidity are obtained for symmetric $2$-dimensional bar-joint frameworks with either $\ell^1$ or $\ell^\infty$ 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.

Keywords


Tree packings; Spanning trees; Bar-joint framework; Infinitesimal rigidity; Symmetric framework; Minkowski geometry

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