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FPSAC 2011, Reykjavík, Iceland DMTCS proc. AO
Develin and Sturmfels showed that regular triangulations of ∆n−1 × ∆ d−1 can be thought of as tropical polytopes. Tropical oriented matroids were defined by Ardila and Develin, and were conjectured to be in bijection with all subdivisions of ∆n−1 × ∆ d−1. In this paper, we show that any triangulation of ∆n−1 × ∆ d−1 encodes a tropical oriented matroid. We also suggest a new class of combinatorial objects that may describe all subdivisions of a bigger class of polytopes. Résumé. Develin etfatcat:2t3ba476dval7efw4jbucjurhu