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    Rights statement: 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.

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An improved bound for the rigidity of linearly constrained frameworks

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<mark>Journal publication date</mark>4/05/2021
<mark>Journal</mark>SIAM Journal on Discrete Mathematics
Issue number2
Volume35
Number of pages6
Pages (from-to)928–933
Publication StatusPublished
<mark>Original language</mark>English

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.

Bibliographic note

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.