Puente Muñoz, Maria Jesus de la and Ansola Fernández-Enríquez, Maria Macarena (2009) A Note on Tropical Triangles in the Plane. Acta Mathematica Sinica. English Series., 25 (11). pp. 1775-1786. ISSN 1439-8516
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Official URL: http://0-www.springerlink.com.cisne.sim.ucm.es/content/104538/
Abstract
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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Tropical triangles, Tropical triangulation, Linear inequalities, Convexity, Tropical semi-field |
| Subjects: | Sciences > Mathematics > Algebraic geometry |
| ID Code: | 12801 |
| Deposited On: | 01 Jun 2011 13:26 |
| Last Modified: | 01 Jun 2011 13:26 |
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