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For a language $L$, we consider its cyclic closure, and more generally thelanguage $C^k(L)$, which consists of all words obtained by partitioning wordsfrom $L$ into $k$ factors and permuting them. We prove that the classes of ET0Land EDT0L languages are closed under the operators $C^k$. This both sharpensand generalises Brandst\"adt's result that if $L$ is context-free then $C^k(L)$is context-sensitive and not context-free in general for $k\geq 3$. We alsoshow that the cyclic closure of an indexed language is indexed.

Permutations of context-free, ET0L and indexed languages