Write $\Psi$ as the Parikh map--i.e., $\Psi(w) = \{(\#_\sigma(w))_{\sigma\in \Sigma}\vert w\in L\}$, where $\#_\sigma(w)$ is the number of times $\sigma$ appears in $w$. It's well-known that, for a CFL $L$, $\Psi(L)$ is a semilinear set (this is Parikh's theorem). Some other interesting things are known, but I have found nothing about the Parikh map of a context-sensitive language. In particular,
what can I say about $\Psi(L_2 - L_1)$ or $\Psi(\bar{L}_1)$ if $L_1, L_2$ are context-free? For instance, if I let $\phi(L) = \{\sum_\sigma \#_\sigma(w)\vert w\in L\} = \{|w| \vert w\in L\}$, is it possible that there is a CFL $L$ such that $\phi(\bar{L}) = \{n!\vert n\in \mathbb{N}\}$? (or any other 'increasing' sequence converging in $\hat{\mathbb{Z}}$, for that matter.)