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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

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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An improved bound for the rigidity of linearly constrained frameworks. / Jackson, Bill; Nixon, Anthony; Tanigawa, Shin-Ichi.
In: SIAM Journal on Discrete Mathematics, Vol. 35, No. 2, 04.05.2021, p. 928–933.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Jackson, B, Nixon, A & Tanigawa, S-I 2021, 'An improved bound for the rigidity of linearly constrained frameworks', SIAM Journal on Discrete Mathematics, vol. 35, no. 2, pp. 928–933. https://doi.org/10.1137/20M134304X

APA

Jackson, B., Nixon, A., & Tanigawa, S-I. (2021). An improved bound for the rigidity of linearly constrained frameworks. SIAM Journal on Discrete Mathematics, 35(2), 928–933. https://doi.org/10.1137/20M134304X

Vancouver

Jackson B, Nixon A, Tanigawa S-I. An improved bound for the rigidity of linearly constrained frameworks. SIAM Journal on Discrete Mathematics. 2021 May 4;35(2):928–933. doi: 10.1137/20M134304X

Author

Jackson, Bill ; Nixon, Anthony ; Tanigawa, Shin-Ichi. / An improved bound for the rigidity of linearly constrained frameworks. In: SIAM Journal on Discrete Mathematics. 2021 ; Vol. 35, No. 2. pp. 928–933.

Bibtex

@article{062cf7d27cb74ec9b47b975124435bbe,
title = "An improved bound for the rigidity of linearly constrained frameworks",
abstract = "We consider the problem of characterising the generic rigidity of bar-jointframeworks in Rdin 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 2010and 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. Weextend the latter result by showing that the given characterisation holds whenever d ≥ 2t.",
keywords = "rigidity, linearly constrained framework, pinned framework, count matroid",
author = "Bill Jackson and Anthony Nixon and Shin-Ichi Tanigawa",
note = "First Published in SIAM Journal on Discrete Mathematics in 35 (2), 2021published by the Society for Industrial and Applied Mathematics (SIAM) Copyright {\textcopyright} by SIAM. Unauthorized reproduction of this article is prohibited.",
year = "2021",
month = may,
day = "4",
doi = "10.1137/20M134304X",
language = "English",
volume = "35",
pages = "928–933",
journal = "SIAM Journal on Discrete Mathematics",
issn = "0895-4801",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "2",

}

RIS

TY - JOUR

T1 - An improved bound for the rigidity of linearly constrained frameworks

AU - Jackson, Bill

AU - Nixon, Anthony

AU - Tanigawa, Shin-Ichi

N1 - 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.

PY - 2021/5/4

Y1 - 2021/5/4

N2 - We consider the problem of characterising the generic rigidity of bar-jointframeworks in Rdin 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 2010and 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. Weextend the latter result by showing that the given characterisation holds whenever d ≥ 2t.

AB - We consider the problem of characterising the generic rigidity of bar-jointframeworks in Rdin 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 2010and 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. Weextend the latter result by showing that the given characterisation holds whenever d ≥ 2t.

KW - rigidity

KW - linearly constrained framework

KW - pinned framework

KW - count matroid

U2 - 10.1137/20M134304X

DO - 10.1137/20M134304X

M3 - Journal article

VL - 35

SP - 928

EP - 933

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

SN - 0895-4801

IS - 2

ER -