Hook length

Given a Young diagram $𝜆$ , the hook at $(𝑖, 𝑗)$ is given by

𝐻 𝜆 (𝑖, 𝑗) = {(𝑝, 𝑞) \in 𝜆 : 𝑝 \geq 𝑖, 𝑞 \geq 𝑗}

and the hook length $ℎ 𝜆 (𝑖, 𝑗)$ is the number of cells in $𝐻 𝜆 (𝑖, 𝑗)$ . comb