Inductive Constructions for Frameworks on a Two-Dimensional Fixed Torus

@article{Ross2015InductiveCF,
  title={Inductive Constructions for Frameworks on a Two-Dimensional Fixed Torus},
  author={Elissa Ross},
  journal={Discrete & Computational Geometry},
  year={2015},
  volume={54},
  pages={78-109}
}
  • Elissa Ross
  • Published 2015
  • Mathematics, Computer Science
  • Discrete & Computational Geometry
  • An infinite periodic framework in the plane can be represented as a framework on a torus, using a $${\mathbb {Z}}^2$$Z2-labelled gain graph. We find necessary and sufficient conditions for the generic minimal rigidity of frameworks on the two-dimensional fixed torus $${\mathcal {T}}_0^2$$T02. It is also shown that every minimally rigid periodic orbit framework on $${\mathcal {T}}_0^2$$T02 can be constructed from smaller frameworks through a series of inductive constructions. These are fixed… CONTINUE READING

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