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How to draw tropical planes. (English) Zbl 1195.14080
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.

##### 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
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