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arXiv · 1906.06686

Signed tropical convexity

Georg Loho·László A. Végh
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Abstract

We establish a new notion of tropical convexity for signed tropical numbers. We provide several equivalent descriptions involving balance relations and intersections of open halfspaces as well as the image of a union of polytopes over Puiseux series and hyperoperations. Along the way, we deduce a new Farkas lemma and Fourier-Motzkin elimination without the non-negativity restriction on the variables. This leads to a Minkowski-Weyl theorem for polytopes over the signed tropical numbers.

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Georg Loho, László A. Végh. 2019-06-16. Signed tropical convexity. https://arxiv.org/abs/1906.06686

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