On the number of distinct block sizes in partitions of a set
It is proved that the average number of distinct block sizes in a partition of a set of n elements is asymptotic to e log n as \(n\to \infty\) and almost all partitions have approximately e log n distinct block sizes. It is well known that the average total number of blocks in a partition is \(\sim\) n/log n as \(n\to \infty\).
scientific article; zbMATH DE number 3918370