English

When is a planar rod configuration infinitesimally rigid?

Combinatorics 2022-04-28 v2

Abstract

We provide a way of determining the infinitesimal rigidity of rod configurations realizing a rank two incidence geometry in the Euclidean plane. We model each rod with a cone over its point set and prove that the resulting geometric realization of the incidence geometry is infinitesimally rigid in regular position if and only if the resulting cone graph is infinitesimally rigid in generic position. This is a generalization of the Molecular conjecture.

Keywords

Cite

@article{arxiv.2112.01960,
  title  = {When is a planar rod configuration infinitesimally rigid?},
  author = {Signe Lundqvist and Klara Stokes and Lars-Daniel Öhman},
  journal= {arXiv preprint arXiv:2112.01960},
  year   = {2022}
}

Comments

17 pages, 4 figures

R2 v1 2026-06-24T08:03:17.389Z