[[Numeric partition]]
# Young diagram

A **Young diagram** is a graphical portrayal of a [[Numeric partition]] as rows of left aligned boxes[^tr]. #m/def/comb
If $(\lambda_{i})_{i=1}$ is a partition then the corresponding Young diagram has $\lambda_{i}$ boxes on the $i$th row.

[^tr]: Some author use different conventions, but this is by far the most  widespread.

Below are all partitions of $4$ in ascending order.
```
[ ]    [ ][ ]    [ ][ ]    [ ][ ][ ]    [ ][ ][ ][ ]
[ ]    [ ]       [ ][ ]    [ ]
[ ]    [ ]
[ ]
```

## Further terminology

- A modified version is a [[Young tableau]], which contains numbers in the boxes.
- [[Hook length]]

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#state/tidy | #lang/en | #SemBr