structural:scholar_edition, information:extraction
Moments of fixed points of random permutations

Let the random variable X be the number of fixed points of a uniformly distributed random permutation of a finite set of size m. Then the n th moment of X is

Note: The upper bound of summation is m, not n.

In other words, the n th moment of this probability distribution is the number of partitions of a set of size n into no more than m parts.This is proved in the article on random permutation statistics, although the notation is a bit different.