Number systems, tilings and seminumerical algorithms

The thesis deals with so-called shift radix systems and their relation to canonical number systems and beta-expansions. In the first part the finiteness property is treated (i.e., under which conditions all elements of a set can be represented in a finite way). It turns out that such an analysis is rather difficult. In the second part SRS-tiles are introduced, i.e., tiles that are induced by shift radix systems in a canonical way. It is shown that there is a linear connection between SRS-tiles and tiles associated to expanding polynomials (tiles associated to Pisot numbers, respectively). Finally variations of shift radix systems (so-called epsilon-shift radix systems) are presented and investigated. Surprisingly the finiteness property seems to be much easier to characterise here.