A generalisation of Sylvester's problem to higher dimensions

2016/08/10 by Simeon Ball, Ball, Simeon, Joaquim Monserrat +1
Computer Science · Engineering · #51M04 #52C35 #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1608.03189

openalex publication_date 2016/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the Number of Ordinary Lines Determined by n Points

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