More colourful simplices (Q629837)

The paper is concerned with simplicial and colourful simplicial depths relative to a~set~\(K\). Any point of the convex hull of each of \((d+1)\) sets of \((d+1)\) points in general position in~\({\mathbb R}^n\) is shown to be contained in at least \(\lceil (d+1)^2/2\rceil\) simplices with one vertex from each set. This improves the available lower bounds for all \(d\geq 4\).