Standard Young tableaux

1. Definition

A standard (Young) tableau of a partition $\lambda \vdash n $ is a bijection between the positive integers $\{1,2,\dots, n\}$ and the cells (also known as boxes) of the Young diagram of $\lambda$, such that rows and columns are increasing. (English convention). A standard tableau of size $n$ is a standard tableau of a partition of size $n$.

2. Notation

By $\mathcal{ST}_n$, we denote the collection of all standard tableaux of $n$.

3. Examples

Here is another example from $\mathcal{ST}_9$.

$\begin{matrix}1 & 4 & 8\\2 & 5 & 9\\3 & 6\\7\\\end{matrix}$ which in Sage input form is $[[1,4,8], [2,5,9],[3,6],[7]]$.

4. Properties

5. Remarks

6. Statistics

7. Maps

8. Known Statistical Dependencies

9. References

10. Sage examples

StandardTableaux (last edited 2014-02-14 09:29:36 by PerAlexandersson)