5 papers
Rigidity on compact surfaces through hyperbolic symmetries
Sean Dewar, Alison La Porta, Rebecca Monks +3
Generically the rigidity of bar-joint structures admits combinatorial characterisations in the Euclidean plane and, more generally, for frameworks on the sphere and the torus. The…
Angular constraints on planar frameworks
Sean Dewar, Georg Grasegger, Anthony Nixon +4
Consider a collection of points in the plane and the sets of slopes or directions of the lines between pairs of points. It is known that the algebraic matroid on the set of directi…
Single-cell 3D genome reconstruction in the haploid setting using rigidity theory
Sean Dewar, Georg Grasegger, Kaie Kubjas +2
This article considers the problem of 3-dimensional genome reconstruction for single-cell data, and the uniqueness of such reconstructions in the setting of haploid organisms. We c…
Triangulated spheres with holes in triangulated surfaces
Katie Clinch, Sean Dewar, Niloufar Fuladi +6
Let denote a sphere with holes. Given a triangulation of a surface , we consider the question of when contains a spanning subgraph such t…
Generalised ErdÅs distance theory on graphs
Sean Dewar, Nora Frankl, Samuel Mansfield +3
The famous ErdÅs distinct distances problem asks the following: how many distinct distances must exist between a set of points in the plane? There are many generalisations of…