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math.CO2025
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…
math.CO2025
From dual canonical bases to positroidal subdivisions
Jian-Rong Li, Ayush Kumar Tewari
The Grassmannian cluster algebra admits a distinguished basis known as the dual canonical basis, whose elements correspond to rectangular semi-standar…
stat.ML2025
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…