Tropical oriented matroids

Abstract

Tropical oriented matroids (as defined by Ardila and Develin) are a tropical analogue of classical oriented matroids in the sense that they encode the properties of the types of points in an arrangement of tropical hyperplanes—in much the same way as the covectors of (classical) oriented matroids describe the types in arrangements of linear hyperplanes.They are in correspondence with other objects of interest in discrete geometry: subdivisions of products of simplices and mixed subdivisions of simplices.The details for this work are provided in Horn (A topological representation theorem for tropical oriented matroids: part I, 2012. arXiv:12120714 [math.CO]; part II, 2012. arXiv:12122080 [math.CO]); see also Horn (DMTCS Proc. 01, 135–146, 2012).