A note on tropical triangles in the plane

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dc.creatorAnsola, M.
dc.creatorde la Puente, M. J.
dc.date2007-01-08
dc.date2008-10-16
dc.date.accessioned2026-07-07T10:10:28Z
dc.date.available2026-07-07T10:10:28Z
dc.descriptionWe 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 $\infty,0,1$. 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.
dc.description15 pages, 2 figures. The paper has been fully revised and enlarged. Tropical triangles called transversal here, were called proper and stable in a previous version. To appear in Acta Math. Sinica (English series)
dc.identifierhttps://arxiv.org/abs/math/0701222
dc.identifierhttp://arxiv.org/abs/math/0701222
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171612
dc.subjectCombinatorics
dc.subject52C35; 52C20; 15A39; 12K99
dc.titleA note on tropical triangles in the plane
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