  Based on the vertex operator realization of the Schur functions, a
determinant-type plethystic Murnaghan-Nakayama rule is obtained and used to
derive a general formula of the expansion coefficient of $s_{\nu}$ in the
plethysm product $s_{\lambda}\circ s_{\mu}$. As an application, we provide a
simple way to compute generalized Warring formula.
