Solution
= Solution
For the staircase $\delta=(m,m-1,\ldots,1)$,
$$
h_{i,j}(\delta)=2(m+1-i-j)+1
$$
whenever $(i,j)$ is a cell, so every hook length is odd. A removable rim hook of length $k$ corresponds to a hook of length $k$ in the original diagram. If a cycle type $\mu$ contains an even part $k$, apply the <Murnaghan–Nakayama rule> to that part first. There are no terms in the sum, and therefore $\chi^\delta(\mu)=0$.