### Impacto

### Downloads

Downloads per month over past year

Puente Muñoz, María Jesús 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

Preview |
PDF
278kB |

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: | 20 Jan 2016 15:00 |

### Origin of downloads

Repository Staff Only: item control page