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One brick at a time: a survey of inductive constructions in rigidity theory

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter (peer-reviewed) › peer-review

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One brick at a time: a survey of inductive constructions in rigidity theory. / Nixon, Anthony; Ross, Elissa.
Rigidity and symmetry. ed. / Robert Connelly; Asia Weiss; Walter Whiteley. New York: Springer, 2014. p. 303-324 (Fields Institute Communications; Vol. 70).

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter (peer-reviewed) › peer-review

Harvard

Nixon, A & Ross, E 2014, One brick at a time: a survey of inductive constructions in rigidity theory. in R Connelly, A Weiss & W Whiteley (eds), Rigidity and symmetry. Fields Institute Communications, vol. 70, Springer, New York, pp. 303-324. https://doi.org/10.1007/978-1-4939-0781-6_15

APA

Nixon, A., & Ross, E. (2014). One brick at a time: a survey of inductive constructions in rigidity theory. In R. Connelly, A. Weiss, & W. Whiteley (Eds.), Rigidity and symmetry (pp. 303-324). (Fields Institute Communications; Vol. 70). Springer. https://doi.org/10.1007/978-1-4939-0781-6_15

Vancouver

Nixon A, Ross E. One brick at a time: a survey of inductive constructions in rigidity theory. In Connelly R, Weiss A, Whiteley W, editors, Rigidity and symmetry. New York: Springer. 2014. p. 303-324. (Fields Institute Communications). doi: 10.1007/978-1-4939-0781-6_15

Author

Nixon, Anthony ; Ross, Elissa. / One brick at a time : a survey of inductive constructions in rigidity theory. Rigidity and symmetry. editor / Robert Connelly ; Asia Weiss ; Walter Whiteley. New York : Springer, 2014. pp. 303-324 (Fields Institute Communications).

Bibtex

@inbook{67e61ec0785348368ef001090c6c274f,
title = "One brick at a time: a survey of inductive constructions in rigidity theory",
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.",
keywords = "Rigidity, Bar-joint framework, Inductive construction",
author = "Anthony Nixon and Elissa Ross",
year = "2014",
doi = "10.1007/978-1-4939-0781-6_15",
language = "English",
isbn = "9781493907809",
series = "Fields Institute Communications",
publisher = "Springer",
pages = "303--324",
editor = "Robert Connelly and Asia Weiss and Walter Whiteley",
booktitle = "Rigidity and symmetry",

}

RIS

TY - CHAP

T1 - One brick at a time

T2 - a survey of inductive constructions in rigidity theory

AU - Nixon, Anthony

AU - Ross, Elissa

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Rigidity

KW - Bar-joint framework

KW - Inductive construction

U2 - 10.1007/978-1-4939-0781-6_15

DO - 10.1007/978-1-4939-0781-6_15

M3 - Chapter (peer-reviewed)

SN - 9781493907809

T3 - Fields Institute Communications

SP - 303

EP - 324

BT - Rigidity and symmetry

A2 - Connelly, Robert

A2 - Weiss, Asia

A2 - Whiteley, Walter

PB - Springer

CY - New York

ER -