9 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…
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…
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…
Transversal matroids and the half plane property
Ayush Kumar Tewari
We focus on checking the validity of the half-plane property on two prominent classes of transversal matroids, namely lattice path matroids and bicircular matroids. We show that la…
Positroids, Dressian and stable polynomials
Ayush Kumar Tewari
Our work is motivated by the connection established between Lorentzian polynomials and the Dressian in the seminal work of Brändén and Huh on Lorentzian polynomials. We analyze thi…
Lattice path matroidal subdivisions, Positive Tropical Grassmannian and Amplituhedron
Ayush Kumar Tewari, Ahmed Umer Ashraf
We introduce the notion of lattice path matroidal subdivisions, or LPM subdivisions for short, and show that these subdivisions are regular and hence the weight vectors for them li…
Moduli dimensions of lattice polygons
Marino Echavarria, Max Everett, Shinyu Huang +5
Given a lattice polygon with interior lattice points, we associate to it the moduli space of tropical curves of genus with Newton polygon . We completely classify th…