English

Tropical Convexity

Metric Geometry 2007-05-23 v3 Combinatorics

Abstract

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 .

Keywords

Cite

@article{arxiv.math/0308254,
  title  = {Tropical Convexity},
  author = {Mike Develin and Bernd Sturmfels},
  journal= {arXiv preprint arXiv:math/0308254},
  year   = {2007}
}

Comments

20 pages, 6 figures