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Documenta Mathematica
Article . 2004 . Peer-reviewed
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arXiv.org e-Print Archive
Preprint . 2003
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Article . 2004
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https://dx.doi.org/10.48550/ar...
Article . 2003
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Tropical convexity

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2004Embargo end date: 01 Jan 2003Publisher:European Mathematical Society - EMS - Publishing House GmbHJournal:Documenta Mathematica, volume 9, pages 1-27 (issn: 1431-0635, eissn: 1431-0643, Copyright policy )Funded by:NSF | New Directions in Computa...
Authors: Mike Develin; Bernd Sturmfels;

doi: 10.4171/dm/154 , 10.48550/arxiv.math/0308254

arXiv: math/0308254

Tropical convexity

Abstract

The notions of convexity and convex polytopes are introduced in the setting of tropical geometry. Combinatorial types of tropical polytopes are shown to be in bijection with regular triangulations of products of two simplices. Applications to phylogenetic trees are discussed.

Related Organizations
Keywords

52A30; 92B10, 52A30, Metric Geometry (math.MG), tropical convexity, \(n\)-dimensional polytopes, phylogenetic trees, regular subdivisions of a product of simplices, Mathematics - Metric Geometry, tropical geometry, 92B10, Tilings in \(n\) dimensions (aspects of discrete geometry), FOS: Mathematics, Mathematics - Combinatorics, Three-dimensional polytopes, Variants of convex sets (star-shaped, (\(m, n\))-convex, etc.), Combinatorics (math.CO), tropical polytopes

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 172
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Top 1%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 Top 1%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    		 Top 10%
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
172
Top 1%
Top 1%
Top 10%
Green
Published in a Diamond OA journal