# Major index of skew-SYT

For a standard Young tableaux (SYT), I can compute the major index as follows:

```
T = Tableau([[1,2,3],[4,5]])
T.major_index()
```

Is there a way to compute the major index of a skew-SYT currently? Something like:

```
S = SkewTableaux().from_expr([[1,1],[[5],[3,4],[1,2]]])
S.major_index()
```

At the moment, it seems major_index() is not defined for the SkewTableau-class.

EDIT: The major index of a (skew) standard Young tableau $T$, denoted $\mathrm{maj}(T)$, is defined as follows. A descent of $T$ is an entry $i$ such that $i+1$ appears strictly below $i$ in $T$. Define $\mathrm{maj}(T)$ as the sum of all descents of $T$. For example, the major index of the skew standard Young tableau above is $2+4=6$.

FindStat has a definition, although they only define it for non-skew tableau. But the definition extends trivially to skew-shapes as well.

Can you give a reference to a (mathematical) definition?

Added the definition of major index.