A quadratic lower bound for colourful simplicial depth

Tamon Stephen () and Hugh Thomas ()
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Tamon Stephen: Simon Fraser University
Hugh Thomas: University of New Brunswick

Journal of Combinatorial Optimization, 2008, vol. 16, issue 4, No 2, 324-327

Abstract: Abstract We show that any point in the convex hull of each of (d+1) sets of (d+1) points in ℝ d is contained in at least ⌊(d+2)2/4⌋ simplices with one vertex from each set.

Keywords: Computational geometry; Carathéodory theorem; Colourful Carathéodory theorem; Simplicial depth; Colourful simplicial depth (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10878-008-9149-x

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