Tropical hyperplane arrangements and oriented matroids

Federico Ardila, Mike Develin

Published 2007-06-20, updated 2007-06-25Version 2

We study the combinatorial properties of a tropical hyperplane arrangement. We define tropical oriented matroids, and prove that they share many of the properties of ordinary oriented matroids. We show that a tropical oriented matroid determines a subdivision of a product of two simplices, and conjecture that this correspondence is a bijection.