Partitions
How many ways are there of expressing 4 as a sum of positive integers? Five if the summands are in (weakly) decreasing order: 4 = 3+1 = 2+2 = 2+1+1 = 1+1+1+1. What about 5 or 6? The sums above are called partitions of 4 and there are many interesting questions concerning counting partitions with various properties. In this video, we give a little teaser introduction to this fascinating theory by finding the generating function for partitions whose only parts are 1, 2 or 3. You can find more material on the Extension III Mathematics website.