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# Now, suppose that is a partition of n. Let d be the side length of its Durfee square (i. it is a d d square), and call this the Durfee length of .

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Let D(n, d) be the number of (n, d)-Durfee matrices.

Prove that for all positive integers n and d, we have pdur(n, d) = D(n, d).

Hint: how many squares are in the "diagonal" of the Durfee square of a partition?