Suho Oh ; Hwanchul Yoo

Triangulations of $\Delta_{n1} \times \Delta_{d1}$ and Tropical Oriented Matroids
dmtcs:2947 
Discrete Mathematics & Theoretical Computer Science,
January 1, 2011,
DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)

https://doi.org/10.46298/dmtcs.2947
Triangulations of $\Delta_{n1} \times \Delta_{d1}$ and Tropical Oriented Matroids
Authors: Suho Oh ; Hwanchul Yoo
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Suho Oh;Hwanchul Yoo
Develin and Sturmfels showed that regular triangulations of $\Delta_{n1} \times \Delta_{d1}$ 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 $\Delta_{n1} \times \Delta_{d1}$. In this paper, we show that any triangulation of $\Delta_{n1} \times \Delta_{d1}$ 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.