0
$\begingroup$

what is a bijective proof of #93 in the link provided http://math.mit.edu/~rstan/bij.pdf:

The number of partitions of $n$ with $k$ parts equals the number of partitions of $n + \binom{k}{2}$ with $k$ distinct parts

  • 0
    Fixed the link, which didn't work as given. My previous comment stands: the notes at the original link give the desired bijection. It includes a picture illustrating the idea, which @Thomas has given in his answer.2012-05-01

1 Answers 1

1

If $a_1\leq a_2 \leq a_3 ... \leq a_k$ is a partition of $n$ then $a_1 < a_2+1 < a_3+2 <... < a_k + {k-1}$ is a partition of $n+0+1+2+...+k-1 = n+\binom{k}{2}$

  • 0
    Thank $y$ou! i appreciate $y$our help2012-05-01