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