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math.CO2025
Generalised Erdős distance theory on graphs
Sean Dewar, Nora Frankl, Samuel Mansfield +3
The famous Erdős 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 t…
math.CO2025
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…