2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132245We 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.20 pages, 7 figures, best viewed in colorCombinatorics52C35; 52C40; 52C22text