Hello I have a doubt about the next partition identities
$P(n: even \; number \; of \; odd \; parts)=P(n: distinct\; parts, \; number \; of \; odd\; parts\; is\; even)$
Also for the case when both instances of "even" are changed to odd.
I need to show a bijection of but I can't figure out how. I have been trying with one example (n=6) to see any particular characteristic however I can not have the equality.
I trying to solve the problem by using a bijection between the partitions of each side because I am not allowed to use function now.
So, any hint would be appreciated!