Tropical and Ordinary Convexity Combined

Details Tropical and Ordinary Convexity Combined Tropical and Ordinary Convexity Combined

2008-01-31

arxiv.org/abs/0801.4835v3

Mathematics

Combinatorics

revised proof of Theorem 7; a few more results and references added

Scientific paper

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.

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