Before revision: Our analysis relies on a close relationship of this problem to some intrinsic properties of random permutations related to the rencontres number (which is the number of n-permutations with a given number of fixed points) .
After revision: Our analysis relies on a close relationship of such problems to some intrinsic properties of random permutations related to the rencontres number (which is the number of n-permutations with a given number of fixed points) .