A note on tropical triangles in the plane

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...

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Veröffentlicht in:Acta mathematica Sinica. English series 2009-11, Vol.25 (11), p.1775-1786
Hauptverfasser: Ansola, M., de la Puente, M. J.
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-009-7345-y