6 papers
Tree metrics and log-concavity for matroids
Federico Ardila-Mantilla, Sergio Cristancho, Graham Denham +3
We show that a set function satisfies the gross substitutes property if and only if its homogeneous generating polynomial is a Lorentzian polynomial for all positive…
Bounded ratios for Lorentzian matrices
Daoji Huang, June Huh, Daniel Soskin +1
We study multiplicative inequalities among entries of Lorentzian matrices, referred to as bounded ratios. These inequalities can be viewed as generalizations of the classical Alexa…
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…
Linear operators preserving volume polynomials
Lukas Grund, June Huh, Mateusz Michałek +2
Volume polynomials measure the growth of Minkowski sums of convex bodies and of tensor powers of positive line bundles on projective varieties. We show that Aluffi's covolume polyn…
Realizations of homology classes and projection areas
Daoji Huang, June Huh, Mateusz Michałek +2
The relationship between convex geometry and algebraic geometry has deep historical roots, tracing back to classical works in enumerative geometry. In this paper, we continue this…