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arXiv · 0906.3377

Block-diagonalized rigidity matrices of symmetric frameworks and applications

Bernd Schulze
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Abstract

In this paper, we give a complete self-contained proof that the rigidity matrix of a symmetric bar and joint framework (as well as its transpose) can be transformed into a block-diagonalized form using techniques from group representation theory. This theorem is basic to a number of useful and interesting results concerning the rigidity and flexibility of symmetric frameworks. As an example, we use this theorem to prove a generalization of the Fowler-Guest symmetry extension of Maxwell's rule which can be applied to both injective and non-injective realizations in all dimensions.

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Bernd Schulze. 2009-06-18. Block-diagonalized rigidity matrices of symmetric frameworks and applications. https://arxiv.org/abs/0906.3377

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