Rigidity of symmetric frameworks in normed spaces
Citation
Kitson, D., Nixon, A. and Schulze, B. (2020) 'Rigidity of symmetric frameworks in normed spaces', Linear Algebra and its Applications, 607, 231-285, available: https://doi.org/10.1016/j.laa.2020.08.004
Date
2020-12-15Author
Kitson, Derek
Nixon, Anthony
Schulze, Bernd
Peer Reviewed
YesMetadata
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Kitson, D., Nixon, A. and Schulze, B. (2020) 'Rigidity of symmetric frameworks in normed spaces', Linear Algebra and its Applications, 607, 231-285, available: https://doi.org/10.1016/j.laa.2020.08.004
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 lp spaces with p not equal to 2). Complete combinatorial characterisations are obtained for half-turn rotation in the l1 and l-infinity plane. As a key tool, a new Henneberg-type inductive construction is developed for the matroidal class of (2,2,0)-gain-tight gain graphs.
Keywords
Bar-joint frameworkInfinitesimal rigidity
Gain graphs
Matroids
Normed spaces