1. For i > n, the ith moment is smaller than that of that Poisson distribution. Specifically, for i ≤ n, the ith moment is the ith Bell number, i.e. the number of partitions of a set of size i. Limiting probability distribution As the size of the permuted set grows, we get This is just the probability that a Poisson-distributed random variable with expected value 1 is equal to k. In other words, as n grows, the probability distribution of the number of fixed points of a random permutation of a set of size n approaches the Poisson distribution with expected value 1. See also Oberwolfach problem, a different mathematical problem involving the arrangement of diners at tables Problème des ménages, a similar problem involving partial derangements References Riordan, John, An Introduction to Combinatorial Analysis, New York, Wiley, 1958, pages 57, 58, and 65. Permutations Discrete distributions Fixed points (mathematics) Triangles of numbers Theory of probability distributions