Tropical and Ordinary Convexity Combined
Combinatorics
2010-03-24 v3 Commutative Algebra
Abstract
A polytrope is a tropical polytope which at the same time is convex in the ordinary sense. A -dimensional polytrope turns out to be a tropical simplex, that is, it is the tropical convex hull of points. This statement is equivalent to the known fact that the Segre product of two full polynomial rings (over some field ) 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.
Keywords
Cite
@article{arxiv.0801.4835,
title = {Tropical and Ordinary Convexity Combined},
author = {Michael Joswig and Katja Kulas},
journal= {arXiv preprint arXiv:0801.4835},
year = {2010}
}
Comments
revised proof of Theorem 7; a few more results and references added