On the Finiteness property of negative cubic Pisot bases
  We study arithmetical aspects of Ito-Sadahiro number systems with negative base. We show that the bases $-\beta<-1$, where $\beta$ is zero of $x^3-mx^2-mx-m,\ m\in\mathbb N,$ possess the so-called finiteness property. For the Tribonacci base $-\gamma,$ zero of $x^3-x^2-x-1$, we present an effective algorithm for addition and subtraction. In particular, we present a finite state transducer performing these operations. As a consequence of the structure of the transducer, we determine the maximal number of fractional digits arising from addition or subtraction of two $(-\gamma)$-integers. 
Tom\'a\v{s} V\'avra
math.CO