Artículos de revistas
Tropicalization of facets of polytopes
Fecha
2017-06Registro en:
Allamigeon, Xavier; Katz, Ricardo David; Tropicalization of facets of polytopes; Elsevier Science Inc; Linear Algebra and its Applications; 523; 6-2017; 79-101
0024-3795
CONICET Digital
CONICET
Autor
Allamigeon, Xavier
Katz, Ricardo David
Resumen
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.