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On Periodic Alternate Base Expansions
Émilie Charlier, Célia Cisternino, Savinien Kreczman
For an alternate base , we show that if all rational numbers in the unit interval have periodic expansions with respect to the shifts…
A full characterization of Bertrand numeration systems
Émilie Charlier, Célia Cisternino, Manon Stipulanti
Among all positional numeration systems, the widely studied Bertrand numeration systems are defined by a simple criterion in terms of their numeration languages. In 1989, Bertrand-…
Spectrum, algebraicity and normalization in alternate bases
Émilie Charlier, Célia Cisternino, Zuzana Masáková +1
The first aim of this article is to give information about the algebraic properties of alternate bases determining sofic systems. We show that a…
Combinatorial properties of lazy expansions in Cantor real bases
Célia Cisternino
The lazy algorithm for a real base is generalized to the setting of Cantor bases introduced recently by Charlier and the author. To do so…