hook length

The hook length of a partition $λ$ at $x = (i, j) \in λ$ (in the Young tableau(x)) is defined as

h (x) = h (i, j) = λ_{i} + λ_{j}^{'} - i - j + 1

(where $λ_{j}^{'}$ is the conjugate partition)

In other words, it counts the number of boxes to the right and below the box (including the box).

Properties