  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.
