Complex Pisot Numeration Systems

Multiple points of tilings associated with Pisot numeration systems

This paper deals with a kind of aperiodic tilings associated with Pisot numeration systems, originally due to W.P. Thurston, in the formulation of S. Akiyama. We treat tilings whose generating Pisot units are cubic and not totally real. Each such tiling gives a numeration system on the complex plane; we can express each complex number z in the following form: z= ck −k + ck−1 −k+1 + · · · + c1 −...

Self aÆne tiling and Pisot numeration system

Numeration Systems

Automata and Numeration Systems ∗

This article is a short survey on the following problem: given a set X ⊆ N, find a “simple algorithm” accepting X and rejecting N \ X. By simple algorithm, we mean a finite automaton, a substitution, a logical formula, . . . We will see that these algorithms strongly depend on the way one represents the integers. However, once the base of representation is fixed, these models are all equivalent...

Boundary of Central Tiles Associated with Pisot Beta-numeration and Purely Periodic Expansions

This paper studies tilings related to the β-transformation when β is a Pisot number (that is not supposed to be a unit). Then it applies the obtained results to study the set of rational numbers having a purely periodic β-expansion. Secial focus is given to some quadratic examples.