Tropicalization of facets of polytopes

Abstract : It is known that any tropical polytope is the image under the valuation map of ordinary polytopes over the Puiseux series field. The latter polytopes are called lifts of the tropical polytope. We prove that any pure tropical polytope is the intersection of the tropical half-spaces given by the images under the valuation map of the facet-defining half-spaces of a certain lift. We construct this lift explicitly, taking into account geometric properties of the given polytope. Moreover, when the generators of the tropical polytope are in general position, we prove that the above property is satisfied for any lift. This solves a conjecture of Develin and Yu.
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Linear Algebra and its Applications, Elsevier, 2017, 〈10.1016/j.laa.2017.02.011〉
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https://hal.inria.fr/hal-01096435
Contributeur : Xavier Allamigeon <>
Soumis le : mercredi 17 décembre 2014 - 14:57:30
Dernière modification le : mercredi 25 avril 2018 - 10:45:37

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Xavier Allamigeon, Ricardo D. Katz. Tropicalization of facets of polytopes. Linear Algebra and its Applications, Elsevier, 2017, 〈10.1016/j.laa.2017.02.011〉. 〈hal-01096435〉

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