2007/01/08 by M. Ansola, Ansola, M., M. J. de la Puente +1
Computer Science · Mathematics · #12K99 #15A39 #52C20 #52C35 #Advanced Differential Equations and Dynamical Systems #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.math/0701222
openalex publication_date 2007/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ∞,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.