
6
Mean and Insensitive. Random
Permutations.
6.1 The Probabilistic Viewpoint
In the previous chapters we have enumerated permutations according to var-
ious statistics. A similar line of research is to choose an n-permutation p at
random, and compute the probability of the event that p has a given property
A. Throughout this chapter, when we say that we select an n-permutation
at random, we mean that each of the n! permutations of length n are chosen
with probability 1/n!.
Theoretically speaking, this is not a totally new approach. Indeed, the
probability of success (that is, the event that p has property A) is defined as
the number of favorable outcomes ...