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A Note on Tropical Triangles in the Plane

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dc.contributor.authorPuente Muñoz, María Jesús De La
dc.contributor.authorAnsola Fernández-Enríquez, María Macarena
dc.date.accessioned2023-06-20T00:05:48Z
dc.date.available2023-06-20T00:05:48Z
dc.date.issued2009
dc.description.abstractWe 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.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipMTM
dc.description.sponsorshipUCM
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/12801
dc.identifier.doi10.1007/s10114-009-7345-y
dc.identifier.issn1439-8516
dc.identifier.officialurlhttp://0-www.springerlink.com.cisne.sim.ucm.es/content/104538/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/41950
dc.issue.number11
dc.journal.titleActa Mathematica Sinica. English Series.
dc.language.isoeng
dc.page.final1786
dc.page.initial1775
dc.publisherSpringer Verlag
dc.relation.projectID2005–02865
dc.relation.projectID910444
dc.rights.accessRightsopen access
dc.subject.cdu512.7
dc.subject.keywordTropical triangles
dc.subject.keywordTropical triangulation
dc.subject.keywordLinear inequalities
dc.subject.keywordConvexity
dc.subject.keywordTropical semi-field
dc.subject.ucmGeometria algebraica
dc.subject.unesco1201.01 Geometría Algebraica
dc.titleA Note on Tropical Triangles in the Plane
dc.typejournal article
dc.volume.number25
dspace.entity.typePublication
relation.isAuthorOfPublication630e203d-3f7d-46d6-a43c-cb07da8c4b71
relation.isAuthorOfPublication.latestForDiscovery630e203d-3f7d-46d6-a43c-cb07da8c4b71

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