6 papers
The genus of configuration curves of planar linkages is generically odd
Josef Schicho, Ayush Kumar Tewari, Audie Warren
A one-degree-of-freedom graph is a graph obtained from a minimally rigid graph in the plane and removing an edge. For such graph, the set of realisations with fixed edge length, mo…
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…
Irreducible components of sets of points in the plane that satisfy distance conditions
Niels Lubbes, Mehdi Makhul, Josef Schicho +1
For a given graph whose edges are labeled with general real numbers, we consider the set of functions from the vertex set into the Euclidean plane such that the distance between th…
Generalised ErdÅs distance theory on graphs
Sean Dewar, Nora Frankl, Samuel Mansfield +3
The famous ErdÅs 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…
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…
On the Genus of One Degree of Freedom Planar Linkages via Tropical Geometry
Josef Schicho, Ayush Kumar Tewari, Audie Warren
This paper focuses on studying the configuration spaces of graphs realised in , such that the configuration space is, after normalisation, one dimensional. If this is…