7
$\begingroup$

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)

$\endgroup$
10
$\begingroup$

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 $n$.

$\endgroup$
  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.