A Note on Tropical Triangles in the Plane  

作　　者：M.ANSOLA M.J.de la PUENTE 

机构地区：[1]Departamento de Algebra Facultad de Matemáticas, Universidad Complutense

出　　处：《Acta Mathematica Sinica,English Series》2009年第11期1775-1786,共12页数学学报（英文版）

基　　金：supported by MTM 2005-02865;UCM 910444

摘　　要：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.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.

关 键 词：tropical triangles tropical triangulation linear inequalities CONVEXITY tropical semi-field 

分 类 号：O187[理学—数学]