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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)

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1 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 $n$.

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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
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