Geodesic
Tropical convexity
Documenta mathematica, Tome 9 (2004), pp. 1-27
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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.
DOI : 10.4171/dm/154
Classification : 52A30, 92B10 
@article{10_4171_dm_154,
     author = {Mike Develin and Bernd Sturmfels},
     title = {Tropical convexity},
     journal = {Documenta mathematica},
     pages = {1--27},
     year = {2004},
     volume = {9},
     doi = {10.4171/dm/154},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/154/}
}
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Mike Develin; Bernd Sturmfels. Tropical convexity. Documenta mathematica, Tome 9 (2004), pp. 1-27. doi: 10.4171/dm/154

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