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Discrete Mathematics & Theoretical Computer Science |
Develin and Sturmfels showed that regular triangulations of $\Delta_{n-1} \times \Delta_{d-1}$ 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 $\Delta_{n-1} \times \Delta_{d-1}$. 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.
Source : ScholeXplorer
IsRelatedTo ARXIV math/0605598 Source : ScholeXplorer IsRelatedTo DOI 10.1016/j.aim.2007.02.014 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.math/0605598
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