Colorful Simplicial Depth, Minkowski Sums, and Generalized Gale Transforms
Colorful Simplicial Depth, Minkowski Sums, and Generalized Gale Transforms
Abstract The colorful simplicial depth of a collection of $d+1$ finite sets of points in Euclidean $d$-space is the number of choices of a point from each set such that the origin is contained in their convex hull. We use methods from combinatorial topology to prove a tight upper bound …