Suho Oh ; Hwanchul Yoo
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Triangulations of $\Delta_{n-1} \times \Delta_{d-1}$ 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)
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https://doi.org/10.46298/dmtcs.2947
Triangulations of $\Delta_{n-1} \times \Delta_{d-1}$ and Tropical Oriented MatroidsArticle
Authors: Suho Oh 1; Hwanchul Yoo 1
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Suho Oh;Hwanchul Yoo
1 Department of Mathematics [MIT]
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.
R. Ehrenborg;G. Hetyei;M. Readdy, 2020, Classification Of Uniform Flag Triangulations Of The Boundary Of The Full Root Polytope Of Type A, arXiv (Cornell University), 163, 2, pp. 462-511, 10.1007/s10474-020-01099-2, http://arxiv.org/abs/1901.07113.