1 citations · 1 across the 9 of their papers we have counts for
9 papers
The number of realisations of a random graph
Sean Dewar, Anthony Nixon, Ben Smith
Determining the number of realisations, up to isometries, of a graph for a specific choice of edge lengths is a fundamental problem in discrete geometry. In this article we prove t…
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…
A counter-example to Baranyai's combinatorial characterisation for 3-rigidity
Sean Dewar
Recently Baranyai described a necessary combinatorial characterisation of graph rigidity for dimension 3. In this short note we provide a counter-example to the converse of the con…
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…
Extremal decompositions of tropical varieties and relations with rigidity theory
Farhad Babaee, Sean Dewar, James Maxwell
Extremality and irreducibility constitute fundamental concepts in mathematics, particularly within tropical geometry. While extremal decomposition is typically computationally hard…