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dc.contributor.authorAichholzer, Oswin
dc.contributor.authorFabila Monroy, Ruy
dc.contributor.authorHackl, Thomas
dc.contributor.authorHuemer, Clemens
dc.contributor.authorUrrutia Galicia, Jorge
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
dc.identifier.citationAichholzer, O. [et al.]. Empty monochromatic simplices. "Discrete and computational geometry", 01 Març 2014, vol. 51, núm. 2, p. 362-393.
dc.description.abstractLet S be a k-colored (finite) set of n points in , da parts per thousand yen3, in general position, that is, no (d+1) points of S lie in a common (d-1)-dimensional hyperplane. We count the number of empty monochromatic d-simplices determined by S, that is, simplices which have only points from one color class of S as vertices and no points of S in their interior. For 3a parts per thousand currency signka parts per thousand currency signd we provide a lower bound of and strengthen this to Omega(n (d-2/3)) for k=2.; On the way we provide various results on triangulations of point sets in . In particular, for any constant dimension da parts per thousand yen3, we prove that every set of n points (n sufficiently large), in general position in , admits a triangulation with at least dn+Omega(logn) simplices.
dc.format.extent32 p.
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta
dc.subject.lcshComputer science--Mathematics
dc.subject.otherColored point sets
dc.subject.otherEmpty monochromatic simplices
dc.subject.otherHigh dimensional triangulations
dc.subject.otherSimplicial complex
dc.subject.otherConvex polygons
dc.subject.otherPoint sets
dc.titleEmpty monochromatic simplices
dc.subject.lemacInformàtica -- Matemàtica
dc.subject.lemacAnàlisi numèrica
dc.contributor.groupUniversitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta
dc.rights.accessOpen Access
dc.description.versionPostprint (author’s final draft)
upcommons.citation.authorAichholzer, O.; Fabila, R.; Hackl, T.; Huemer, C.; URRUTIA, J.
upcommons.citation.publicationNameDiscrete and computational geometry

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