On the spread of random interleavers

For a given blocklength we determine the number of interleavers which have spread equal to two. Using this, we find out the probability that a randomly chosen interleaver has spread two. We show that as blocklength increases, this probability increases but very quickly converges to the value 1 - e^-2 ap 0.8647. Subsequently, we determine a lower bound on the probability of an interleaver having spread at least s. We show that this lower bound converges to the value e^-2(s-2)2, as the blocklength increases