Given d+1 sets S1,S2,…,Sd+1 (called color classes) in Rd, a simplex is called colorful, if all its vertices are in different color classes. The number of colorful simplices containing a point p∈Rd is known as the colorful simplicial depth of p. Since the point with the maximal depth can be seen as a higher dimensional analogue to median, the colorful simplicial depth is studied not only in discrete and computational geometry, but also in statistics and data analysis. The first result concernin…