On the Average Number of Maxima in a Set of Vectors

Abstract Any of n vectors in d -space is called maximal if none of the remaining vectors dominates it in every component. Assuming that n vectors are distributed identically and that the d components of each vector are distributed independently and continuously, we determine the expected number of maximal vectors explicitly for any n and d . The asymptotic behaviour of this quantity as n tends to infinity, which was investigated by Bentley, Kung, Schkolnick, Thompson and Devroye, follows immediately from our result.