2019/06/16 by Georg Loho, Loho, Georg, László A. Végh +1
Computer Science · Mathematics · #14T05 #52A30 #90C05 #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Optimization and Control (math.OC) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1906.06686
openalex publication_date 2019/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.