We introduce certain torus-equivariant classes on permutohedral varieties which we call
“tautological classes of matroids” as a new geometric framework for studying matroids …

We introduce a presentation of the Chow ring of a matroid by a new set of generators, called
“simplicial generators.” These generators are analogous to nef divisors on projective toric …

Abstract In [3], Nathan Bowler and the first author introduced a category of algebraic objects
called tracts and defined the notion of (weak and strong) matroids over a tract. In the first part …

If $ G $ is a finite graph, a proper coloring of $ G $ is a way to color the vertices of the graph
using $ n $ colors so that no two vertices connected by an edge have the same color.(The …

OSCAR is an innovative new computer algebra system which combines and extends the
power of its four cornerstone systems-GAP (group theory), Singular (algebra and algebraic …

We study moduli spaces of rational weighted stable tropical curves, and their connections
with Hassett spaces. Given a vector has only heavy and light entries. In this case, the tropical …

The goal of this paper is to introduce a construction of a vector bundle on a tropical variety.
When the base is a tropical toric variety these tropicalize toric vector bundles, and are …

The classical volume polynomial in algebraic geometry measures the degrees of ample
(and nef) divisors on a smooth projective variety. We introduce an analogous volume …

Matroids are combinatorial abstractions of independence, a ubiquitous notion that pervades
many branches of mathematics. June Huh and his collaborators recently made spectacular …

A matroid is a fundamental and actively studied object in combinatorics. Matroids generalize
linear dependency in vector spaces as well as many aspects of graph theory. Moreover …