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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…
Computing the number of realisations of a rigid graph
Sean Dewar, Georg Grasegger, Josef Schicho +2
A graph is said to be rigid if, given a generic realisation of the graph as a bar-and-joint framework in the plane, there exist only finitely many other realisations of the graph w…
Algebraic connectivity in normed spaces
James Cruickshank, Sean Dewar, Derek Kitson
The algebraic connectivity of a graph in a finite dimensional real normed linear space is a geometric counterpart to the Fiedler number of the graph and can be regarded as…
Uniquely realisable graphs in polyhedral normed spaces
Sean Dewar
A framework (a straight-line embedding of a graph into a normed space allowing edges to cross) is globally rigid if any other framework with the same edge lengths with respect to t…
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…