Non-Generic Tropical Hyperplane Arrangements and the Secondary polytope of $\Delta_{n-1} \times \Delta_{d-1}$

Lindsay C. Piechnik

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arXiv · 1010.1446

Non-Generic Tropical Hyperplane Arrangements and the Secondary polytope of $\Delta_{n-1} \times \Delta_{d-1}$

Lindsay C. Piechnik

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Abstract

Ardila and Develin's paper on tropical oriented hyperplane arrangements and tropical oriented matroids defines tropical oriented matroids and conjectures a bijection between them and triangulations of products of simplices $\Delta_{n-1} \times \Delta_{d-1}$. Oh and Yoo recently confirmed this conjecture; however, neither group addressed the case of hyperplanes that are not in generic position. These non-generic arrangements do not correspond to tropical oriented matroids, but they encode information about subdivisions of $\Delta_{n-1} \times \Delta_{d-1}$. This note considers the non-generic case and presents some preliminary results in the area.

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BibTeX RIS

Lindsay C. Piechnik. 2010-10-07. Non-Generic Tropical Hyperplane Arrangements and the Secondary polytope of $\Delta_{n-1} \times \Delta_{d-1}$. https://arxiv.org/abs/1010.1446

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