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.
['Antoine Deza', 'Tamon Stephen', 'Feng Xie']
More Colourful Simplices