Pretty much want to show that the number partitions of n into no more than k terms equals the number partitions of n into any number of terms, each one not exceeding k.
I was given the hint that you can use reflections in y=-x of a Youngs diagram to show this. And I think that means you can create a 1 to 1 correspondence between the 2 partitions by swapping the rows and columns of the diagram to get the other one. But I don't really see how you can then use that to show the statement to be true.