Permutation Cycles

We consider permutations of the numbers 1,..., N for some N. By permutation we mean a rearrangment of the number 1,...,N. For example 2 4 5 1 7 6 3 8 is a permutation of 1,2,...,8. Of course, 1 2 3 4 5 6 7 8 is also a permutation of 1,2,...,8. We can "walk around" a permutation in a interesting way and here is how it is done for the permutation above: Start at position 1. At positi