23 citations · 183 across the 65 of their papers we have counts for
9 papers · 1 filter
The parity module of a matroid
Tom Braden, June Huh, Jacob P. Matherne +2
We introduce the parity module of a matroid with coefficients in a field . When has characteristic zero, we show that the parity module of a matroid is iso…
Matroid correspondence
Colin Crowley, Changxin Ding, Haoxi Hu +7
Motivated by algebraic correspondences and linear operators associated with volume and Lorentzian polynomials, we introduce matroid correspondences and their polymatroid analogues.…
Vertex Posets, Monotone Path Polytopes, and Chow Polynomials
Mateusz Michałek, Leonid Monin, Botong Wang
Let be a convex polytope and let be a linear functional which is nonconstant on every edge of . The induced acyclic orientation determines positive…
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…
The Bergman fan of a polymatroid
Colin Crowley, June Huh, Matt Larson +2
We introduce the Bergman fan of a polymatroid and prove that the Chow ring of the Bergman fan is isomorphic to the Chow ring of the polymatroid. Using the Bergman fan, we establish…