Frameworks with coordinated edge motions

Bernd Schulze; Hattie Serocold; Louis Simon Theran

doi:10.1137/20M1377539

Frameworks with coordinated edge motions

Bernd Schulze, Hattie Serocold, Louis Simon Theran

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We develop a rigidity theory for bar-joint frameworks in Euclidean d-space in which specified classes of edges are allowed to change length in a coordinated fashion that requires differences of lengths to be preserved within each class. Rigidity for these coordinated frameworks is a generic property, and we characterize the rigid graphs in terms of redundant rigidity in the standard d-dimensional rigidity matroid. We also interpret our main results in terms of matroid unions.

Original language	English
Pages (from-to)	2602-2618
Number of pages	17
Journal	SIAM Journal on Discrete Mathematics
Volume	36
Issue number	4
DOIs	https://doi.org/10.1137/20M1377539
Publication status	Published - 9 Nov 2022

Keywords

Coordinated constraint relaxation
Bar-joint frameworks
Rigidity
Infinitesimal rigidity
Rigidity matroid

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10.1137/20M1377539

Schulze_2022_SIAM-DM_Frameworks-coordinated_AAM
Copyright © 2022 Society for Industrial and Applied Mathematics. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1137/20M1377539.
Accepted author manuscript, 331 KBLicence: CC BY

http://arxiv.org/abs/1807.05376

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abstract = "We develop a rigidity theory for bar-joint frameworks in Euclidean d-space in which specified classes of edges are allowed to change length in a coordinated fashion that requires differences of lengths to be preserved within each class. Rigidity for these coordinated frameworks is a generic property, and we characterize the rigid graphs in terms of redundant rigidity in the standard d-dimensional rigidity matroid. We also interpret our main results in terms of matroid unions.",

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N2 - We develop a rigidity theory for bar-joint frameworks in Euclidean d-space in which specified classes of edges are allowed to change length in a coordinated fashion that requires differences of lengths to be preserved within each class. Rigidity for these coordinated frameworks is a generic property, and we characterize the rigid graphs in terms of redundant rigidity in the standard d-dimensional rigidity matroid. We also interpret our main results in terms of matroid unions.

AB - We develop a rigidity theory for bar-joint frameworks in Euclidean d-space in which specified classes of edges are allowed to change length in a coordinated fashion that requires differences of lengths to be preserved within each class. Rigidity for these coordinated frameworks is a generic property, and we characterize the rigid graphs in terms of redundant rigidity in the standard d-dimensional rigidity matroid. We also interpret our main results in terms of matroid unions.

KW - Coordinated constraint relaxation

KW - Bar-joint frameworks

KW - Rigidity

KW - Infinitesimal rigidity

KW - Rigidity matroid

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JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

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Frameworks with coordinated edge motions

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Keywords

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