4 papers
The number of realisations of a random graph
Sean Dewar, Anthony Nixon, Ben Smith
Determining the number of realisations of a graph for a specific choice of edge lengths is a fundamental problem in discrete geometry. In this article we prove that the -dimensi…
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…
Counting fibres of the Hadamard product using Bergman fans
Oliver Clarke, Sean Dewar, Matteo Gallet +3
We study the generic fibre of the Hadamard product of linear spaces via matroid theory and tropical geometry. To do so, we introduce the flip product, a numerical invariant associa…
A tropical approach to rigidity: counting realisations of frameworks
Oliver Clarke, Sean Dewar, Daniel Green Tripp +4
A realisation of a graph in the plane as a bar-joint framework is rigid if there are finitely many other realisations, up to isometries, with the same edge lengths. Each of these f…