Young Diagram

A Young diagram, also called a Ferrers Diagram, represents Partitions as patterns of dots, with the $n$th row having the same number of dots as the $n$th term in the Partition. A Young diagram of the Partition

$$n=a+b+\ldots+c,$$

for a list $a$, $b$, ..., $c$ of $k$ Positive Integers with $a\geq b\geq\ldots\geq c$ is therefore the arrangement of $n$ dots or square boxes in $k$ rows, such that the dots or boxes are left-justified, the first row is of length $a$, the second row is of length $b$, and so on, with the $k$th row of length $c$. The above diagram corresponds to one of the possible partitions of 100.

See also Durfee Square, Hook Length Formula, Partition, Partition Function P, Young Tableau

References

Messiah, A. Appendix D in Quantum Mechanics, 2 vols. Amsterdam, Netherlands: North-Holland, p. 1113, 1961-62.