&bgr;-expansions and symbolic dynamics
Theoretical Computer Science - Conference on arithmetics and coding systems, Marseille-Luminy, June 1987
Confluent linear numeration systems
Theoretical Computer Science
Automata, Languages, and Machines
Automata, Languages, and Machines
Multiple points of tilings associated with Pisot numeration systems
Theoretical Computer Science
On-line odometers for two-sided symbolic dynamical systems
DLT'02 Proceedings of the 6th international conference on Developments in language theory
Theoretical Computer Science
| Hi-index | 5.23 |
We study @a-adic expansions of numbers, that is to say, left infinite representations of numbers in the positional numeration system with the base @a, where @a is an algebraic conjugate of a Pisot number @b. Based on a result of Bertrand and Schmidt, we prove that a number belongs to Q(@a) if and only if it has an eventually periodic @a-adic expansion. Then we consider @a-adic expansions of elements of the ring Z[@a^-^1] when @b satisfies the so-called Finiteness property (F). We give two algorithms for computing these expansions - one for positive and one for negative numbers. In the particular case that @b is a quadratic Pisot unit satisfying (F), we inspect the unicity and/or multiplicity of @a-adic expansions of elements of Z[@a^-^1]. We also provide algorithms to generate @a-adic expansions of rational numbers in that case.