9 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…
Stable cuts, NAC-colourings and flexible realisations of graphs
Katie Clinch, Dániel Garamvölgyi, John Haslegrave +3
A (2-dimensional) realisation of a graph is a pair , where maps the vertices of to . A realisation is flexible if it can be continuously deformed w…
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…
The -dimensional realisation number of a rigid graph
Sean Dewar, Anthony Nixon, Ben Smith
Determining the number of (complex) realisations of a rigid graph for a specific choice of edge lengths is a fundamental problem in discrete geometry. In this article we provide tw…
The -fold circuit property for matroids
Bill Jackson, Anthony Nixon, Ben Smith
Double circuits were introduced by Lovász in 1980 as a fundamental tool in his derivation of a min-max formula for the size of a maximum matching in linear matroids. This formula…
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…