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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

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Volume 10, Issue 2 (Jan 2010)


Tropical and ordinary convexity combined

Michael Joswig / Katja Kulas
Published Online: 2010-03-10 | DOI: https://doi.org/10.1515/advgeom.2010.012


A polytrope is a tropical polytope which at the same time is convex in the ordinary sense. A d-dimensional polytrope turns out to be a tropical simplex, that is, it is the tropical convex hull of d + 1 points. This statement is equivalent to the known fact that the Segre product of two full polynomial rings (over some field K) has the Gorenstein property if and only if the factors are generated by the same number of indeterminates. The combinatorial types of polytropes up to dimension three are classified.

About the article

Received: 2008-02-02

Revised: 2008-05-19

Revised: 2010-02-13

Published Online: 2010-03-10

Published in Print: 2010-04-01

Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom.2010.012. Export Citation

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