An improved bound for the rigidity of linearly constrained frameworks

Jackson, Bill and Nixon, Anthony and Tanigawa, Shin-Ichi (2021) An improved bound for the rigidity of linearly constrained frameworks. SIAM Journal on Discrete Mathematics, 35 (2). 928–933. ISSN 0895-4801

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Abstract

We consider the problem of characterising the generic rigidity of bar-joint frameworks in R d in which each vertex is constrained to lie in a given affine subspace. The special case when d = 2 was previously solved by I. Streinu and L. Theran in 2010 and the case when each vertex is constrained to lie in an affine subspace of dimension t, and d ≥ t(t − 1) was solved by Cruickshank, Guler and the first two authors in 2019. We extend the latter result by showing that the given characterisation holds whenever d ≥ 2t.

Item Type:

Journal Article

Journal or Publication Title:

SIAM Journal on Discrete Mathematics

Additional Information:

First Published in SIAM Journal on Discrete Mathematics in 35 (2), 2021published by the Society for Industrial and Applied Mathematics (SIAM) Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

Uncontrolled Keywords:

/dk/atira/pure/subjectarea/asjc/2600/2600

Subjects:

?? rigiditylinearly constrained frameworkpinned frameworkcount matroidgeneral mathematicsmathematics(all) ??

Departments:

Faculty of Science and Technology > Mathematics and Statistics

ID Code:

152781

Deposited By:

ep_importer_pure

Deposited On:

15 Mar 2021 10:05

Refereed?:

Yes

Published?:

Published

Last Modified:

25 Sep 2024 00:54

URI:

https://eprints.lancs.ac.uk/id/eprint/152781