Let the Durfee Square of length $d$ of a partition of $n$ be the largest square that can be fit into the Ferrer's shape. Call the blocks in the Ferrer's shape on the right of the partition's Durfee Square the arm of that partition, and call the blocks below the Durfee Square the leg of that partition.
a. What can I say about the arm and the leg of a partition of $n$ with Durfee square ($d$ x $d$)? I'm given a hint: "The arm of a partition is itself a partition of______, with the restriction that______." and the same for the leg.
b. Using a, how would I write a generating function of $S_d(x)$ for the sequence $S_{d,n}$ which is the number of partitions of $n$ with Durfee length $d$.
Attempt: I tried looking at the Ferrers shapes of $n=5$ and $d=2$ which are: $5=3+2$ and $5=2+2+1$ but I don't quite see the restriction in part a.