Non-Generic Tropical Hyperplane Arrangements and the Secondary polytope of Δₙ₋₁ × Δd₋₁
Piechnik, Lindsay C.
Original · EN
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 Δₙ₋₁ × Δd₋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 Δₙ₋₁ × Δd₋₁. This note considers the non-generic case and presents some preliminary results in the area.
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