The number of partitions of n is equal to the # of the partitions of 2n divided into n parts.
I know that the number of partitions of any integer n into i parts equals the number of partitions of n with the largest part i, but do not know where to go from here, especially how to prove via bijection – any help is appreciated!
(Supp. problem in my intro. combinatorics class)
Best Answer
HINT: Let $\pi$ be a partition of $2n$ into $n$ parts. Throw away one element from each part of $\pi$, and you get a partition of $n$.