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I've studied the Ferrers' diagram. And It's not clear why it's useful, the only property I noticed until now is that once one partition is drawn with a Ferrers' diagram, it's conjugate could show another partition, at least for what I know now, it doesn't seems to be a big deal. So, what's so enlightening that permited this concept to exist until today?

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1 Answer

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The main reason is because partitions are a heavily obscure part of mathematics. Ferrer's Diagrams make it much easier to visualize diagrams. For example, try the following problem:

How many partitions of $12$ are there that have at least four parts, such that the largest, second-largest, third-largest, and fourth-largest parts are respectively greater than or equal to $4,3,2,1$?

Well, this problem can be trivialized using a Ferrer's Diagram. The full solution is left as an exercise to the reader. But overall a big advantage is that there exists a bijection mapping partitions to diagrams.

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