# Bijective Proof: Number of Partitions of 2n into n parts

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)

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 $n$.

• Wow much simpler than what I was thinking of doing. Thanks so much! – user63101 Feb 20 '13 at 9:33
• @user63101: You’re very welcome. – Brian M. Scott Feb 20 '13 at 9:34
• This is awesome! This is so simple! :) By any chance in which book can i read it? – thetha May 4 '18 at 9:15