Bijective Proof - partitions
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
Solution 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 $n+0+1+2+...+k-1 = n+\binom{k}{2}$