Rights statement: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The definitive publisher-authenticated version James Cruickshank, Hakan Guler, Bill Jackson, Anthony Nixon, Rigidity of Linearly Constrained Frameworks, International Mathematics Research Notices, Volume 2020, Issue 12, June 2020, Pages 3824–3840, https://doi.org/10.1093/imrn/rny170 is available online at: https://academic.oup.com/imrn/article-abstract/2020/12/3824/5067960
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Rigidity of linearly constrained frameworks
AU - Cruickshank, James
AU - Guler, Hakan
AU - Jackson, Bill
AU - Nixon, Anthony Keith
N1 - This is a pre-copy-editing, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The definitive publisher-authenticated version James Cruickshank, Hakan Guler, Bill Jackson, Anthony Nixon, Rigidity of Linearly Constrained Frameworks, International Mathematics Research Notices, Volume 2020, Issue 12, June 2020, Pages 3824–3840, https://doi.org/10.1093/imrn/rny170 is available online at: https://academic.oup.com/imrn/article-abstract/2020/12/3824/5067960
PY - 2020/6/1
Y1 - 2020/6/1
N2 - 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. We will extend their characterisation to the case when d ≥ 3 and each vertex is constrained to lie in an affine subspace of dimension t, when t = 1, 2 and also when t ≥ 3 and d ≥ t(t−1). We then point out that results on body-bar frameworks obtained by N. Katoh and S. Tanigawa in 2013 can be used to characterise when a graph has a rigid realisation as a d-dimensional body-bar framework with a given set of linear constraints.
AB - 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. We will extend their characterisation to the case when d ≥ 3 and each vertex is constrained to lie in an affine subspace of dimension t, when t = 1, 2 and also when t ≥ 3 and d ≥ t(t−1). We then point out that results on body-bar frameworks obtained by N. Katoh and S. Tanigawa in 2013 can be used to characterise when a graph has a rigid realisation as a d-dimensional body-bar framework with a given set of linear constraints.
U2 - 10.1093/imrn/rny170
DO - 10.1093/imrn/rny170
M3 - Journal article
VL - 2020
SP - 3824
EP - 3840
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
SN - 1073-7928
IS - 12
ER -