Hook partition
= Hook partition
{title2=$(n-k,1^k)$}
A hook partition has shape $(n-k,1^k)$, $0\leq k\leq n-1$. Equivalently its <Young diagram> has no cell $(2,2)$, so its only cell of content zero is $(1,1)$. Its <standard Young tableaux> are counted by $\binom{n-1}{k}$: choose the $k$ entries below the initial $1$, then the column and remaining row orders are forced.