ABSTRACT
We emphasize that in these definitions the order of the positive integers in the sum is not relevant. For example, 2 + 1 + 3 and 3 + 1 + 2 count as the same partition of 6. The numbers that occur in these partitions are called parts. The standard convention is to write the parts in decreasing order. So the standard way to write this partition of 6 is 3 + 2 + 1. Partitions, as well as being interesting in their own right, have a number of applications to other problems. We hope you will read far enough to see that we make a good deal of use of them in Chapters 13 and 14.
