A generalisation of Sylvester's problem to higher dimensions

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/109014

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor	Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
dc.contributor.author	Ball, Simeon Michael
dc.contributor.author	Monserrat, Joaquim
dc.date	2017-07-01
dc.identifier.citation	Ball, S., Monserrat, J. A generalisation of Sylvester's problem to higher dimensions. "Journal of geometry", 1 Juliol 2017, vol. 108, núm. 2, p. 529-543.
dc.identifier.citation	0047-2468
dc.identifier.citation	10.1007/s00022-016-0357-8
dc.identifier.uri	http://hdl.handle.net/2117/109014
dc.language.iso	eng
dc.relation	info:eu-repo/grantAgreement/ES/1PE/TIN2014-57497-P
dc.rights	Attribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria
dc.subject	Lagrangian points
dc.subject	Sylvester's problem
dc.subject	Green-Tao
dc.subject	Geometria
dc.title	A generalisation of Sylvester's problem to higher dimensions
dc.type	info:eu-repo/semantics/publishedVersion
dc.type	info:eu-repo/semantics/article
dc.description.abstract	In this article we consider $S$ to be a set of points in $d$-space with the property that any $d$ points of $S$ span a hyperplane and not all the points of $S$ are contained in a hyperplane. The aim of this article is to introduce the function $e_d(n)$, which denotes the minimal number of hyperplanes meeting $S$ in precisely $d$ points, minimising over all such sets of points $S$ with $\|S\|=n$.

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