Show that the number of partitions of the integer $n$ is equal to the number of partitions of $2n$ into $n$ parts using a Young Diagram.
I can't seem to figure out any way to create a bijection between these two cases using a Young Diagram.
I'm thinking to maybe create a diagram of the "$n$ into anything" part and then adding an extra row on the bottom of that of length $n$ to create the second half.
Does this work?