Digital expansions with negative real bases

Similarly to Parry's characterization of $\beta$-expansions of real numbers in real bases $\beta > 1$, Ito and Sadahiro characterized digital expansions in negative bases, by the expansions of the endpoints of the fundamental interval. Parry also described the possible expansions of 1 in base $\beta > 1$. In the same vein, we characterize the sequences that occur as $(-\beta)$-expansion of $\frac{-\beta}{\beta+1}$ for some $\beta > 1$. These sequences also describe the itineraries of 1 by linear mod one transformations with negative slope.