Rigidity of symmetric frameworks in normed spaces
Abstract
We develop a combinatorial rigidity theory for symmetric bar-joint frameworks in a general finite dimensional normed space. In the case of rotational symmetry, matroidal Maxwell-type sparsity counts are identified for a large class of $d$-dimensional normed spaces (including all $\ell^p$ spaces with $p\not=2$). Complete combinatorial characterisations are obtained for half-turn rotation in the $\ell^1$ and $\ell^\infty$-plane. As a key tool, a new Henneberg-type inductive construction is developed for the matroidal class of $(2,2,0)$-gain-tight graphs.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2018
- DOI:
- 10.48550/arXiv.1808.04484
- arXiv:
- arXiv:1808.04484
- Bibcode:
- 2018arXiv180804484K
- Keywords:
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- Mathematics - Metric Geometry;
- Mathematics - Combinatorics;
- 52C25;
- 20C35;
- 05C50
- E-Print:
- 42 pages, 11 figures. This version contains corrected proofs and more detailed explanations have been provided for greater clarity