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Tropical hyperplane arrangements and oriented matroids

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Abstract

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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Authors and Affiliations

  1. San Francisco State University, 1600 Holloway Ave., San Francisco, CA, 94132, USA

    Federico Ardila

  2. American Institute of Mathematics, 360 Portage Ave., Palo Alto, CA, USA

    Mike Develin

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  1. Federico Ardila
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  2. Mike Develin
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Correspondence to Federico Ardila.

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Ardila, F., Develin, M. Tropical hyperplane arrangements and oriented matroids. Math. Z. 262, 795–816 (2009). https://doi.org/10.1007/s00209-008-0400-z

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  • DOI: https://doi.org/10.1007/s00209-008-0400-z

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