Tropical Convexity

Details Tropical Convexity Tropical Convexity

2003-08-27

arxiv.org/abs/math/0308254v3

Documenta Math. 9 (2004), 1--27

Mathematics

Metric Geometry

20 pages, 6 figures

Scientific paper

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. Theorem 29 and Corollary 30 in the paper, relating tropical polytopes to injective hulls, are incorrect. See the erratum at http://www.math.uiuc.edu/documenta/vol-09/vol-09-eng.html .

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