Signe Lundqvist
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Signe Lundqvist has a total of 2 co-authors. Here are the top co-authors by number of shared publications:
- Klara Stokes
Department of Mathematics and Mathematical Statistics Umeå University Umeå Sweden
1 shared publication - Lars-Daniel Öhman
Umeå Universitet
1 shared publication
Latest Publications
- Open Access
- 19 December 2023
- Published by Springer Nature in Discrete & Computational Geometry
- Vol. 73 (1) , 25-48
When is a Planar Rod Configuration Infinitesimally Rigid?
We investigate the rigidity properties of rod configurations. Rod configurations are realizations of rank two incidence geometries as points (joints) and straight lines (rods) in the Euclidean plane, such that the lines move as rigid bodies, connected at the points. Note that not all incidence geometries have such realizations. We show that under the assumptions that the rod configuration exists and is sufficiently generic, its infinitesimal rigidity is equivalent to the infinitesimal rigidity of generic frameworks of the graph defined by replacing each rod by a cone over its point set. To put this into context, the molecular conjecture states that the infinitesimal rigidity of rod configurations realizing 2-regular hypergraphs is determined by the rigidity of generic body and hinge frameworks realizing the same hypergraph. This conjecture was proven by Jackson and Jordán in the plane, and by Katoh and Tanigawa in arbitrary dimension. Whiteley proved a version of the molecular conjecture for hypergraphs of arbitrary degree that have realizations as independent body and joint frameworks. Our result extends his result to hypergraphs that do not necessarily have realizations as independent body and joint frameworks, under the assumptions listed above.
- 19 December 2023
- Published by Springer Nature in Discrete & Computational Geometry
- Vol. 73 (1) , 25-48
Open AccessWhen is a Planar Rod Configuration Infinitesimally Rigid?
We investigate the rigidity properties of rod configurations. Rod configurations are realizations of rank two incidence geometries as points (joints) and straight lines (rods) in the Euclidean plane, such that the lines move as rigid bodies, connected at the points. Note that not all incidence geometries have such realizations. We show that under the assumptions that the rod configuration exists and is sufficiently generic, its infinitesimal rigidity is equivalent to the infinitesimal rigidity of generic frameworks of the graph defined by replacing each rod by a cone over its point set. To put this into context, the molecular conjecture states that the infinitesimal rigidity of rod configurations realizing 2-regular hypergraphs is determined by the rigidity of generic body and hinge frameworks realizing the same hypergraph. This conjecture was proven by Jackson and Jordán in the plane, and by Katoh and Tanigawa in arbitrary dimension. Whiteley proved a version of the molecular conjecture for hypergraphs of arbitrary degree that have realizations as independent body and joint frameworks. Our result extends his result to hypergraphs that do not necessarily have realizations as independent body and joint frameworks, under the assumptions listed above.