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Infinitesimal rigidity of symmetric bar-joint frameworks

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Infinitesimal rigidity of symmetric bar-joint frameworks. / Schulze, Bernd; Tanigawa, Shin-ichi.
In: SIAM Journal on Discrete Mathematics, Vol. 29, No. 3, 2015, p. 1259-1286.

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

Harvard

Schulze, B & Tanigawa, S 2015, 'Infinitesimal rigidity of symmetric bar-joint frameworks', SIAM Journal on Discrete Mathematics, vol. 29, no. 3, pp. 1259-1286. https://doi.org/10.1137/130947192

APA

Schulze, B., & Tanigawa, S. (2015). Infinitesimal rigidity of symmetric bar-joint frameworks. SIAM Journal on Discrete Mathematics, 29(3), 1259-1286. https://doi.org/10.1137/130947192

Vancouver

Schulze B, Tanigawa S. Infinitesimal rigidity of symmetric bar-joint frameworks. SIAM Journal on Discrete Mathematics. 2015;29(3):1259-1286. Epub 2015 Jul 30. doi: 10.1137/130947192

Author

Schulze, Bernd ; Tanigawa, Shin-ichi. / Infinitesimal rigidity of symmetric bar-joint frameworks. In: SIAM Journal on Discrete Mathematics. 2015 ; Vol. 29, No. 3. pp. 1259-1286.

Bibtex

@article{923fbac8cc5444deb4b0c60d8daaed40,
title = "Infinitesimal rigidity of symmetric bar-joint frameworks",
abstract = "We propose new symmetry-adapted rigidity matrices to analyze the infinitesimal rigidity of bar-joint frameworks of arbitrary-dimension with Abelian point group symmetries. These matrices define new symmetry-adapted rigidity matroids on group-labeled quotient graphs. Using these new tools, we establish combinatorial characterizations of infinitesimally rigid two-dimensional bar-joint frameworks whose joints are positioned as generically as possible subject to the symmetry constraints imposed by a reflection, a half-turn, or a threefold rotation in the plane. For bar-joint frameworks which are generic with respect to any other cyclic point group in the plane, we provide a number of necessary conditions for infinitesimal rigidity.",
author = "Bernd Schulze and Shin-ichi Tanigawa",
note = "Date of Acceptance: 06/05/2015",
year = "2015",
doi = "10.1137/130947192",
language = "English",
volume = "29",
pages = "1259--1286",
journal = "SIAM Journal on Discrete Mathematics",
issn = "0895-4801",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",

}

RIS

TY - JOUR

T1 - Infinitesimal rigidity of symmetric bar-joint frameworks

AU - Schulze, Bernd

AU - Tanigawa, Shin-ichi

N1 - Date of Acceptance: 06/05/2015

PY - 2015

Y1 - 2015

N2 - We propose new symmetry-adapted rigidity matrices to analyze the infinitesimal rigidity of bar-joint frameworks of arbitrary-dimension with Abelian point group symmetries. These matrices define new symmetry-adapted rigidity matroids on group-labeled quotient graphs. Using these new tools, we establish combinatorial characterizations of infinitesimally rigid two-dimensional bar-joint frameworks whose joints are positioned as generically as possible subject to the symmetry constraints imposed by a reflection, a half-turn, or a threefold rotation in the plane. For bar-joint frameworks which are generic with respect to any other cyclic point group in the plane, we provide a number of necessary conditions for infinitesimal rigidity.

AB - We propose new symmetry-adapted rigidity matrices to analyze the infinitesimal rigidity of bar-joint frameworks of arbitrary-dimension with Abelian point group symmetries. These matrices define new symmetry-adapted rigidity matroids on group-labeled quotient graphs. Using these new tools, we establish combinatorial characterizations of infinitesimally rigid two-dimensional bar-joint frameworks whose joints are positioned as generically as possible subject to the symmetry constraints imposed by a reflection, a half-turn, or a threefold rotation in the plane. For bar-joint frameworks which are generic with respect to any other cyclic point group in the plane, we provide a number of necessary conditions for infinitesimal rigidity.

U2 - 10.1137/130947192

DO - 10.1137/130947192

M3 - Journal article

VL - 29

SP - 1259

EP - 1286

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

SN - 0895-4801

IS - 3

ER -