I have a quick question for anyone familiar with the theory of integer partitions. Because of the geometric series, it is the case that
This is a generating series for a certain class of integer partitions, the partitions where no part is divisible by three. By examining the representation on the right-hand side, it seemed clear to me that this was also the generating series for the partitions of where each even part occurs at most twice, and each odd part occurs at most once.
However, this is apparently wrong, and it is indeed the generating series for the partitions of simply where each part occurs at most twice. My question is this: why? I can’t possibly conceive of a way you could get a partition where 3 occurs twice. Where any even number occurs twice? Sure. But not any odd one. I mean, the language seems to be
So what do you think?