Tropical hyperplane arrangements and oriented matroids
نویسندگان
چکیده
منابع مشابه
Tropical Hyperplane Arrangements and Oriented Matroids
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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The present paper is the first in a series of four dealing with a mapping, introduced by the present authors, from orientations to spanning trees, from regions to simplices in real hyperplane arrangements, from reorientations to bases in oriented matroids (in order of increasing generality). This mapping is actually defined for oriented matroids on a linearly ordered ground set. We call it the ...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2008
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-008-0400-z