How to draw tropical planes. (English) Zbl 1195.14080

Herrmann, Sven; Jensen, Anders; Joswig, Michael; Sturmfels, Bernd

Electron. J. Comb. 16, No. 2, Research Paper R6, 26 p. (2009).

A tropical plane is meant to be a two-dimensional tropical linear subspace in the tropical projective space \(TP^{n-1}\). In this paper, the authors present a bijection between tropical planes and arrangements of metric trees. A Dressian \(Dr(d, n)\) is the tropical prevariety defined by all three term Plucker relation. Various combinatorial results about \(Dr(3, n)\) are given. An extension of the notion of Grassmannians and Dressians from the hypersimplex to arbitrary matroid polytope is given.

Reviewer: Jorge Ramirez Alfonsin (Paris)

MSC:

14T05	Tropical geometry (MSC2010)
52B40	Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)
14M15	Grassmannians, Schubert varieties, flag manifolds
05C05	Trees

Keywords:

tropical plane; metric trees; matroid