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.
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