  Let $\Delta$ be a pure simplicial complex and $I_\Delta$ its Stanley-Reisner
ideal in a polynomial ring $S$. We show that $\Delta$ is a matroid (complete
intersection) if and only if $S/I_\Delta^{(m)}$ ($S/I_\Delta^m$) is clean for
all $m\in\mathbb{N}$. If $\dim(\Delta)=1$, we also prove that
$S/I_\Delta^{(2)}$ ($S/I_\Delta^2$) is clean if and only if $S/I_\Delta^{(2)}$
($S/I_\Delta^2$) is Cohen-Macaulay.
