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 $n$.

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

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