Generating sets of tropical hemispaces
Ricardo D. Katz, Viorel Niţică, Beppo Levi · arXiv (Cornell University) · 2013
We consider tropical hemispaces, dened as tropically convex sets whose complements are also tropically convex, and tropical semispaces, dened as maximal tropically convex sets not containing a given point. We characterize tropical hemispaces by means of generating sets, composed of points and rays, that we call (P;R)-representations. With each hemispace we associate a matrix with coecients in the completed tropical semiring, satisfying an extended rank-one condition. Our proof techniques are based on homogenization (lifting a convex set to a cone), and the relation between tropical hemispaces and semispaces.