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arxiv: math/0512400 · v2 · submitted 2005-12-16 · 🧮 math.CO

A quadratic lower bound for colourful simplicial depth

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keywords boundcolourfulcontainedconvexdepthfloorhullleast
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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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