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Rigidity and Symmetry pp 303–324Cite as

One Brick at a Time: A Survey of Inductive Constructions in Rigidity Theory

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Part of the book series: Fields Institute Communications ((FIC,volume 70))

Abstract

We present a survey of results concerning the use of inductive constructions to study the rigidity of frameworks. By inductive constructions we mean simple graph moves which can be shown to preserve the rigidity of the corresponding framework. We describe a number of cases in which characterisations of rigidity were proved by inductive constructions. That is, by identifying recursive operations that preserved rigidity and proving that these operations were sufficient to generate all such frameworks. We also outline the use of inductive constructions in some recent areas of particularly active interest, namely symmetric and periodic frameworks, frameworks on surfaces, and body-bar frameworks. As the survey progresses we describe the key open problems related to inductions.

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Author information

Authors and Affiliations

  1. School of Mathematics, Heilbronn Institute for Mathematical Research, University of Bristol, Bristol, UK

    A. Nixon

  2. Department of Mathematics and Statistics, York University, Toronto, ON, Canada

    E. Ross

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  1. A. Nixon
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  2. E. Ross
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Correspondence to A. Nixon .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Cornell University, Ithaca, New York, USA

    Robert Connelly

  2. Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada

    Asia Ivić Weiss

  3. Department of Mathematics & Statistics, York University, Toronto, Ontario, Canada

    Walter Whiteley

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Nixon, A., Ross, E. (2014). One Brick at a Time: A Survey of Inductive Constructions in Rigidity Theory. In: Connelly, R., Ivić Weiss, A., Whiteley, W. (eds) Rigidity and Symmetry. Fields Institute Communications, vol 70. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0781-6_15

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