2016
DOI: 10.1007/s00454-015-9755-1
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Gain-Sparsity and Symmetry-Forced Rigidity in the Plane

Abstract: We consider planar bar-and-joint frameworks with discrete point group symmetry in which the joint positions are as generic as possible subject to the symmetry constraint. We provide combinatorial characterizations for symmetry-forced rigidity of such structures with rotation symmetry or dihedral symmetry of order 2k with odd k, unifying and extending previous work on this subject. We also explore the matroidal background of our results and show that the matroids induced by the row independence of the orbit mat… Show more

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Cited by 33 publications
(140 citation statements)
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“…The following count condition appears when analyzing the infinitesimal rigidity of frameworks with dihedral symmetry on the plane [7]:…”
Section: Examples Of Matroidsmentioning
confidence: 99%
See 4 more Smart Citations
“…The following count condition appears when analyzing the infinitesimal rigidity of frameworks with dihedral symmetry on the plane [7]:…”
Section: Examples Of Matroidsmentioning
confidence: 99%
“…In [7] it was shown that the count induces a matroid when Γ is dihedral. The following lemma gives a condition for the corresponding α to be polymatroidal.…”
Section: Examples Of Matroidsmentioning
confidence: 99%
See 3 more Smart Citations