Tropical and Ordinary Convexity Combined

By Michael Joswig, Katja Kulas. 2008

102 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0b2e6ee62000ae9950f280398d48188539d2b593

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In Algebra and Number Theory

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

DRESSIANS, TROPICAL GRASSMANNIANS, AND THEIR RAYS (2011, background): “Shapes that might appear in the tight-span of a matroid subdivision; these precisely are the two-dimensional polytropes [15]”
On visualization scaling, subeigenvectors and Kleene stars in max algebra (2008, background): “z p i ) 1/p for p > 0. Prop. 3.1 raises a question whether or not there exist max cones containing positive vectors, which are ﬁnitely generated and convex, other than Kleene cones. The results of [28] suggest that the answer is negative. Let K be a convex cone, then y ∈ K is called an extremal o”