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A generalisation of Sylvester's problem to higher dimensions

Autor
Ball, S.; Monserrat, J.
Tipus d'activitat
Article en revista
Revista
Journal of geometry
Data de publicació
2017-07-01
Volum
108
Número
2
Pàgina inicial
529
Pàgina final
543
DOI
https://doi.org/10.1007/s00022-016-0357-8 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/109014 Obrir en finestra nova
Resum
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 $|S|=n$.
Citació
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.
Paraules clau
Green-Tao, Sylvester's problem
Grup de recerca
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

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