We show that any point in the convex hull of each of (d +1) sets of (d +1) points in general position in Rd is contained in at least (d + 1)2/2 simplices with one vertex from each ...
We study the expected topological properties of ˇCech and Vietoris-Rips complexes built on random points in Rd . We find higher dimensional analogues of known results for connect...