A note on tropical triangles in the plane

Details A note on tropical triangles in the plane A note on tropical triangles in the plane

2007-01-08

arxiv.org/abs/math/0701222v3

Mathematics

Combinatorics

15 pages, 2 figures. The paper has been fully revised and enlarged. Tropical triangles called transversal here, were called pr

Scientific paper

We define transversal tropical triangles (affine and projective) and characterize them via six inequalities to be satisfied by the coordinates of the vertices. We prove that the vertices of a transversal tropical triangle are tropically independent and they tropically span a classical hexagon whose sides have slopes $\infty,0,1$. Using this classical hexagon, we determine a parameter space for transversal tropical triangles. The coordinates of the vertices of a transversal tropical triangle determine a tropically regular matrix. Triangulations of the tropical plane are obtained.

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