Name: Incidence geometry and universality in the tropical plane
Keywords: General theory of linear incidence geometry and projective geometries, Tropical geometry, tropical geometry, Planar arrangements of lines and pseudolines (aspects of discrete geometry), FOS: Mathematics, incidence geometry, Mathematics - Combinatorics, Newton polygons, universality, Combinatorics (math.CO)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Oct 2018Embargo end date: 01 Jan 2017 English Publisher:Elsevier BVJournal:Journal of Combinatorial Theory, Series A, volume 159, pages 26-53 (issn: 0097-3165,

Authors: Brandt, Milo; Jones, Michelle; Lee, Catherine; Ranganathan, Dhruv;

doi: 10.1016/j.jcta.2018.05.002 , 10.48550/arxiv.1709.00366

arXiv: 1709.00366

Incidence geometry and universality in the tropical plane

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Abstract

We examine the incidence geometry of lines in the tropical plane. We prove tropical analogs of the Sylvester-Gallai and Motzkin-Rabin theorems in classical incidence geometry. This study leads naturally to a discussion of the realizability of incidence data of tropical lines. Drawing inspiration from the von Staudt constructions and Mn��v's universality theorem, we prove that determining whether a given tropical linear incidence datum is realizable by a tropical line arrangement requires solving an arbitrary linear programming problem over the integers.

v2: 20 pages, 20 figures. Final version to appear in Journal of Combinatorial Theory, Series A

Keywords

General theory of linear incidence geometry and projective geometries, Tropical geometry, tropical geometry, Planar arrangements of lines and pseudolines (aspects of discrete geometry), FOS: Mathematics, incidence geometry, Mathematics - Combinatorics, Newton polygons, universality, Combinatorics (math.CO)

2 Research products, page 1 of 1

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