Prague, March 2011

Periodicity and finiteness in non-standard numeration systems

• Beta-expansions

• Pisot numbers, Parry numbers and Perron numbers

• The (F) Property

• Canonical numeration systems

Bibliography

[1] Ch. Frougny, Numeration systems, Chapter 7 in M. Lothaire, Algebraic Combinatorics on Words, Cambridge University Press, 2002.

[2] Ch. Frougny and J. Sakarovitch, Number representation and finite automata, Chapter 2 in Combinatorics, Automata and Number Theory, V. Berthé, M. Rigo (Eds), Cambridge University Press, 2010.

[3] Ch. Frougny and B. Solomyak, Finite beta-expansions, Ergodic Theory & Dynamical Systems 12 (1992) 713-723. Download.