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Block-diagonalized rigidity matrices of symmetric frameworks and applications

Research output: Contribution to journalJournal article

Published

Journal publication date2010
JournalContributions to algebra and geometry
Journal number2
Volume51
Number of pages40
Pages427-466
Original languageEnglish

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 symmetry-extended version of Maxwell's rule given in [FG] which can be applied to both injective and non-injective realizations in all dimensions.