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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…
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…
Positivity sets of hinge functions
Josef Schicho, Ayush Kumar Tewari, Audie Warren
In this paper we investigate which subsets of the real plane are realisable as the set of points on which a one-layer ReLU neural network takes a positive value. In the case of con…