%0 Journal Article
%T Triangulations of $жд_{n-1} \times жд_{d-1}$ and Tropical Oriented Matroids
%A Suho Oh
%A Hwanchul Yoo
%J Mathematics
%D 2010
%I arXiv
%X Develin and Sturmfels showed that regular triangulations of $\Delta_{n-1} \times \Delta_{d-1}$ can be thought as tropical polytopes. Tropical oriented matroids were defined by Ardila and Develin, and were conjectured to be in bijection with all subdivisions of $\Delta_{n-1} \times \Delta_{d-1}$. In this paper, we show that any triangulation of $\Delta_{n-1} \times \Delta_{d-1}$ 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.
%U http://arxiv.org/abs/1009.4750v3