More Colourful Simplices Journal Articles

abstract

• We show that any point in the convex hull of each of (d+1) sets of (d+1) points in general position in \R^d is contained in at least (d+1)^2/2 simplices with one vertex from each set. This improves the known lower bounds for all d >= 4.

authors

• Deza, Antoine
• Stephen, Tamon
• Xie, Feng

status

• published 

publication date

• March 2011

has subject area

• 0101 Pure Mathematics (FoR)
• 0103 Numerical and Computational Mathematics (FoR)
• 0802 Computation Theory and Mathematics (FoR)
• Computation Theory & Mathematics (Science Metrix)

published in

• Discrete and Computational Geometry  Journal

keywords

• Colourful Caratheodory theorem
• Colourful simplicial depth
• Computer Science
• Computer Science, Theory & Methods
• DEPTH
• Discrete geometry
• Mathematics
• Physical Sciences
• Science & Technology
• Technology

Digital Object Identifier (DOI)

• 10.1007/s00454-010-9291-y

start page

• 272

end page

• 278

volume

• 45

issue

• 2