8 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 certain graph associated to a matroid (together with some extra data). Concretely, Tutte's path t…
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 polymat…
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…