6: Groups Acting on Sets

Until now we have thought of permutations mostly as ways of listing the elements of a set. In this chapter we will find it very useful to think of permutations as functions. This will help us in using permutations to solve enumeration problems that cannot be solved by the quotient principle because they involve counting the blocks of a partition in which the blocks don’t have the same size. We begin by studying the kinds of permutations that arise in situations where we have used the quotient principle in the past.