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A Note on Tropical Triangles in the Plane

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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 11:26
Last Modified:06 Feb 2014 09:32

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