How to draw tropical planes
type: Item
instance of: scholarly article
title: How to draw tropical planes
zbMATH Open document ID: 1195.14080
author: Sven Herrmann
author: Michael Joswig
author: Bernd Sturmfels
author: Anders Nedergaard Jensen
published in: The Electronic Journal of Combinatorics
publication date: 2009-07-08T00:00:00Z
full work available at URL: https://arxiv.org/abs/0808.2383
full work available at URL: https://eudml.org/doc/117529
full work available at URL: v16i2r6.html
review text: 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.
Mathematics Subject Classification ID: 14T05
Mathematics Subject Classification ID: 52B40
Mathematics Subject Classification ID: 14M15
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 5576453
zbMATH Keywords: tropical plane
zbMATH Keywords: metric trees
zbMATH Keywords: matroid
reviewed by: Jorge Luis Ramírez Alfonsín
describes a project that uses: Macaulay2
describes a project that uses: polymake
describes a project that uses: cdd
describes a project that uses: Gfan
describes a project that uses: Homology
MaRDI profile type: Publication
arXiv ID: 0808.2383
description: scientific article