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oai:recercat.cat:2117/266622026-01-16T07:29:19Zcom_2072_1033col_2072_452950
RECERCAT author Aichholzer, Oswin author Fabila Monroy, Ruy author Hackl, Thomas author Huemer, Clemens author Urrutia Galicia, Jorge 2014-03-01 Let 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.Postprint (author’s final draft) http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Open Access Attribution-NonCommercial-NoDerivs 3.0 Spain Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta Computer science--Mathematics Colored point sets Empty monochromatic simplices High dimensional triangulations Simplicial complex Convex polygons Point sets Triangles Informàtica -- Matemàtica Anàlisi numèrica Empty monochromatic simplices Article