[[Young tableau]]
# Semi-standard Young tableau

A **semi-standard Young tableau** is a [[Young tableau]] with strictly increasing columns and strictly non-decreasing rows[^kep], #m/def/comb 
as opposed to a standard Young tableau which in addition has strictly increasing rows.

```
[1][1]  [1][2]
[2]     [2]

Semi-standard Young tableaux of shape λ=(2,1) with cells less than 2
```

[^kep]: 2023, [[@keppelerGroupsRepresentations2023|Groups and representations]], §7.2.5, p. 109

## Properties

- The number of semi-standard Young tableaux with each cell $\Theta(i,j) < N$ is given by [[Stanley's hook content formula]].


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