A Topological Representation Theorem for tropical oriented matroids

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:142

Article

Horn, Silke¹ 

[1] Tech Univ Darmstadt, Dolivostr 15, D-64293 Darmstadt, Germany

关键词: Tropical geometry;    Tropical oriented matroids;    Tropical hyperplanes;    Tropical pseudohyperplanes;    Mixed subdivisions;    Topological Representation Theorem;    Oriented matroids;   

DOI  :  10.1016/j.jcta.2016.03.003

来源: Elsevier

【 摘 要 】

Tropical oriented matroids were defined by Ardila and Develin in 2007. They are a tropical analogue of classical oriented matroids in the sense that they encode the properties of the types of points in an arrangement of tropical hyperplanes in much the same way as the covectors of classical oriented matroids describe the types in arrangements of linear hyperplanes. Ardila and Develin proved that tropical oriented matroids can be represented as mixed subdivisions of dilated simplices. In this paper we show that this correspondence is a bijection. Moreover, tropical analogues for the Topological Representation Theorem for classical oriented matroids by Folkman and Lawrence are presented. (C) 2016 Elsevier Inc. All rights reserved.

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