4 citations · 4 across the 7 of their papers we have counts for
8 papers
The phylogenetic rank of a graph
Franklin Ashworth, Oliver Clarke, Jeffrey Giansiracusa +3
The Pachter-Sturmfels phylogenetic rank of a graph G is the minimal number of metric trees needed to embed G isometrically. Here, all edges of G are of length one and the product o…
A lifting partition theorem for tropical tritangent classes to smooth space sextic curves
Maria Angelica Cueto, Hannah Markwig, Yue Ren
The set of tritangent planes to smooth tropical space sextic curves has 15 connected components, recording continuous displacements of planes preserving the tritangency condition.…
Root bounds of vertical systems using tropical geometry
Elisenda Feliu, Paul Alexander Helminck, Oskar Henriksson +3
Sparse polynomial systems with vertical coefficient dependencies arise naturally when describing the critical points of optimization problems and, when augmented with linear forms,…
Tropical methods for building real space sextics with totally real tritangent planes
Maria Angelica Cueto, Yoav Len, Hannah Markwig +1
This paper proposes the use of combinatorial techniques from tropical geometry to build the 120 tritangent planes to a given smooth algebraic space sextic. Although the tropical co…
The tropical galaxy of a Laman graph
Amelia Bielby, Arushi Chauhan, Cassia Pearce +1
A Laman graph is a minimally rigid graph in dimension two, and its realization number is its number of distinct embeddings with fixed generic edge lengths. While conjectured to…
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…
Embedding polynomial systems into vertically parametrised families: A case study on ODEbase
Oliver Daisey, Yue Ren, Yuvraj Singh
Vertically parametrised polynomial systems are a particular nice class of parametrised polynomial systems for which a lot of interesting algebraic information is encoded in its com…
Parallel Computation of tropical varieties, their positive part, and tropical Grassmannians
Dominik Bendle, Janko Boehm, Yue Ren +1
In this article, we present a massively parallel framework for computing tropicalizations of algebraic varieties which can make use of finite symmetries. We compute the tropical Gr…