2 citations · 4 across the 10 of their papers we have counts for
10 papers
Lorentzian polynomials and matroids over triangular hyperfields 2: Analytic aspects
Matthew Baker, June Huh, Mario Kummer +1
Brändén and Huh showed that Lorentzian polynomials unify Hodge-Riemann relations in combinatorics: their supports are M-convex, and every M-convex set supports a Lorentzian polynom…
Flats and hyperplane arrangements for matroids with coefficients
Jannis Koulman, Oliver Lorscheid
Based on the notion of vectors and linear subspaces for a matroid, we develop a theory of flats and hyperplane arrangements for T-matroids, where T is a tract. This leads to severa…
A modern perspective on Tutte's homotopy theorem
Matthew Baker, Tong Jin, Oliver Lorscheid
We begin with a review of Tutte's homotopy theory, which concerns the structure of a certain graph associated to a matroid (together with some extra data). Concretely, Tutte's path…
Lorentzian polynomials and matroids over triangular hyperfields 1: Topological aspects
Matthew Baker, June Huh, Mario Kummer +1
Lorentzian polynomials serve as a bridge between continuous and discrete convexity, connecting analysis and combinatorics. In this article, we study the topology of the space $\mat…
Representation theory for polymatroids
Matthew Baker, June Huh, Donggyu Kim +2
We develop a theory of representations of (discrete) polymatroids over tracts in terms of Plücker coordinates and suitable Plücker relations. As special cases, we recover polymatro…
The foundation of generalized parallel connections, 2-sums, and segment-cosegment exchanges of matroids
Matthew Baker, Oliver Lorscheid, Zach Walsh +1
We show that, under suitable hypotheses, the foundation of a generalized parallel connection of matroids is the relative tensor product of the foundations. Using this result, we sh…
New building blocks for -geometry: bands and band schemes
Matthew Baker, Tong Jin, Oliver Lorscheid
We develop and study a generalization of commutative rings called bands, along with the corresponding geometric theory of band schemes. Bands generalize both hyperrings, in the sen…
Foundations of matroids -- Part 2: Further theory, examples, and computational methods
Matthew Baker, Oliver Lorscheid, Tianyi Zhang
In this sequel to "Foundations of matroids - Part 1", we establish several presentations of the foundation of a matroid in terms of small building blocks. For example, we show that…
On a theorem of Lafforgue
Matthew Baker, Oliver Lorscheid
We give a new proof, along with some generalizations, of a folklore theorem (attributed to Laurent Lafforgue) that a rigid matroid (i.e., a matroid with indecomposable basis polyto…
The topological shadow of F1-geometry: congruence spaces
Oliver Lorscheid, Samarpita Ray
In this paper we introduce congruence spaces, which are topological spaces that are canonically attached to monoid schemes and that reflect closed topological properties. This lead…