Tropical hyperplane arrangements and oriented matroids

Details Tropical hyperplane arrangements and oriented matroids Tropical hyperplane arrangements and oriented matroids

2007-06-20

arxiv.org/abs/0706.2920v2

Mathematics

Combinatorics

20 pages, 7 figures, best viewed in color

Scientific paper

We study the combinatorial properties of a tropical hyperplane arrangement.
We define tropical oriented matroids, and prove that they share many of the
properties of ordinary oriented matroids. We show that a tropical oriented
matroid determines a subdivision of a product of two simplices, and conjecture
that this correspondence is a bijection.

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