Tags: #definition

Young tableau(x)

Given a Young diagram (ex: (3, 3, 2, 1, 1))

We call a tableau(x) on a Young diagram a numbering of the boxes 1 through some $d$.

The standard Young tableaux (SYT) is a tableaux that uses the numbers 1 through $n$ (the weight of the partition) that fills the rows where each box is increasing as you go down and right.

ex:

(but it doesn't have to be in reading order)

We use $f_{\lambda }$ to denote the number of standard Young tableaus of size $\lambda$

Properties

The hook length formula $$
f_\lambda = \frac{n!}{\prod_{b \in \lambda} h(b)}