A quadratic lower bound for colourful simplicial depth

Details A quadratic lower bound for colourful simplicial depth A quadratic lower bound for colourful simplicial depth

2005-12-16

arxiv.org/abs/math/0512400v2

Mathematics

Combinatorics

4 pages, revised style and organization

Scientific paper

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 floor((d+2)^2/4) simplices with one
vertex from each set.

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