In number theory, a Durfee square is an attribute of an integer partition.
A partition of n has a Durfee square of size s if s is the largest number such that the partition contains at least s parts with values ≥ s.[1] An equivalent, but more visual, definition is that the Durfee square is the largest square that is contained within a partition's Ferrers diagram.
In a letter to Arthur Cayley in 1883, Sylvester wrote:[4] "Durfee's square is a great invention of the importance of which its author has no conception.
"The Durfee square method leads to this generating function for the integer partitions: where
The partitions of an integer n contain Durfee squares with sides up to and including