29 citations · 127 across the 14 of their papers we have counts for
14 papers
Tutte polynomials of matroids as universal valuative invariants
Luis Ferroni, Benjamin Schröter
We provide a full classification of all families of matroids that are closed under duality and minors, and for which the Tutte polynomial is a universal valuative invariant. There…
Face enumeration for split matroid polytopes
Luis Ferroni, Benjamin Schröter
This paper initiates the explicit study of face numbers of matroid polytopes and their computation. We prove that, for the large class of split matroid polytopes, their face number…
Valuative invariants for large classes of matroids
Luis Ferroni, Benjamin Schröter
We study an operation in matroid theory that allows one to transition a given matroid into another with more bases via relaxing a \emph{stressed subset}. This framework provides a…
The Merino--Welsh conjecture for split matroids
Luis Ferroni, Benjamin Schröter
In 1999 Merino and Welsh conjectured that evaluations of the Tutte polynomial of a graph satisfy an inequality. In this short article we show that the conjecture generalized to mat…
Ehrhart polynomials of rank two matroids
Luis Ferroni, Katharina Jochemko, Benjamin Schröter
Over a decade ago De Loera, Haws and Köppe conjectured that Ehrhart polynomials of matroid polytopes have only positive coefficients and that the coefficients of the corresponding…
Reconstructibility of matroid polytopes
Guillermo Pineda-Villavicencio, Benjamin Schröter
We specify what is meant for a polytope to be reconstructible from its graph or dual graph. And we introduce the problem of class reconstructibility, i.e., the face lattice of the…
Moduli spaces of codimension-one subspaces in a linear variety and their tropicalization
Philipp Jell, Hannah Markwig, Felipe Rincón +1
We study the moduli space of -dimensional linear subspaces contained in a fixed -dimensional linear variety , and its tropicalization. We prove that these moduli space…
Parametric shortest-path algorithms via tropical geometry
Michael Joswig, Benjamin Schröter
We study parameterized versions of classical algorithms for computing shortest-path trees. This is most easily expressed in terms of tropical geometry. Applications include shortes…
Correlation bounds for fields and matroids
June Huh, Benjamin Schröter, Botong Wang
Let be a finite connected graph, and let be a spanning tree of chosen uniformly at random. The work of Kirchhoff on electrical networks can be used to show that the eve…
Multi-splits and tropical linear spaces from nested matroids
Benjamin Schröter
In this paper we present an explicit combinatorial description of a special class of facets of the secondary polytopes of hypersimplices. These facets correspond to polytopal subdi…
Algorithms for Tight Spans and Tropical Linear Spaces
Simon Hampe, Michael Joswig, Benjamin Schröter
We describe a new method for computing tropical linear spaces and more general duals of polyhedral subdivisions. It is based on Ganter's algorithm (1984) for finite closure systems…
Matroids from hypersimplex splits
Michael Joswig, Benjamin Schröter
A class of matroids is introduced which is very large as it strictly contains all paving matroids as special cases. As their key feature these split matroids can be studied via tec…
The degree of a tropical basis
Michael Joswig, Benjamin Schröter
We give an explicit upper bound for the degree of a tropical basis of a homogeneous polynomial ideal. As an application f-vectors of tropical varieties are discussed. Various examp…
Linear programs and convex hulls over fields of Puiseux fractions
Michael Joswig, Georg Loho, Benjamin Lorenz +1
We describe the implementation of a subfield of the field of formal Puiseux series in polymake. This is employed for solving linear programs and computing convex hulls depending on…