ISBN 9783843910392

978-3-8439-1039-2, Reihe Mathematik

Katja Kulas
Combinatorics of Tropical Polytopes

153 Seiten, Dissertation Technische Universität Darmstadt (2012), Softcover, A5

Zusammenfassung / Abstract

In this thesis we deal with the building blocks of tropical polytopes — the polytropes. These objects are polytopes which are convex in the ordinary and in the tropical sense at the same time. We study their properties in general and for special examples such as the well-known associahedron. A new tropical convex hull algorithm using polytropes is presented and compared to existing methods. We analyze the combinatorial structure of tropical polytopes related to the bases of a matroid. Finally, we propose a definition of the tropical edges and the tropical graph of a tropical polytope.