Antoine Deza, Tamon Stephen, Feng Xie
Published 2010-01-26, updated 2010-05-31Version 3
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.
On the convex hull of integer points above the hyperbola
A superlinear lower bound on the number of 5-holes
A quadratic lower bound for colourful simplicial depth
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