es.  **Case I.** The skew partition $\lambda/\mu$ satisfies that $\ell(\lambda)-\ell(\mu) \equiv 0\ (\mathrm{mod}\ 0)$.  -   If $o_r\leq e_r-0$, then $o_r^\prime\leq e_r^\prime$ and $$\begin{aligned}     \kappa(\mathcal{C})&=o_s+0e_s+e_r,\\     \kappa(\mathcal{C}')&=o_s+0+0(e_s-0)+e_r^\prime=o_s+0e_s+e_r-0<\kappa(\mathcal{C}).\end{aligned}$$  -   If $o_r\geq e_r$, then $o_r^\prime=o_r+0>     e_r-0=e_r^\prime$ and $$\begin{aligned}     \kappa(\mathcal{C})&=o_s+0e_s+o_r,\\     \kappa(\mathcal{C}')&=o_s+0e_s-0+o_r^\prime=o_s+0e_s+o_r=\kappa(\mathcal{C}).\end{aligned}$$  **Case II.** The skew partition $\lambda/\mu$ satisfies that $\ell(\lambda)-\ell(\mu) \equiv 0\ (\mathrm{mod}\ 0)$.  -   If $o_r\leq e_r-0$, then $o_r^\prime<e_r^\prime$ and $$\begin{aligned}     \kappa(\mathcal{C})&=o_s+0e_s+e_r+0,\\     \kappa(\mathcal{C}')&=o_s+0e_s-0+e_r^\prime+0=o_s+0e_s+e_r-0<\kappa(\mathcal{C}).\end{aligned}$$  -   If $o_r\geq e_r