Permutation Groups

Abstract

It might seem odd that we want to discuss group theory in a book on enumeration but it will turn out to be an important tool. If we are counting the number of arrangements of a set of objects, we might wish to count two arrangements which are symmetrical as being the same. A simple example is that of a bracelet made up of different coloured beads. It then makes sense to count two arrangements of the beads as the same if one can be rotated into the other.

We will assume a basic knowledge of the definition of groups as well as an ability to use them in a simple way. This can all be found in one or two books as part of this series.