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math.NT2026
Parry condition, existence and uniqueness of alternate bases
Émilie Charlier, Savinien Kreczman, Zuzana Masáková +1
Alternate bases are a numeration system that generalizes the Rényi numeration system. It is common in this context to construct examples or counter-examples by specifying the expan…
math.NT2025
Numeration systems without a dominant root and regularity
Émilie Charlier, Savinien Kreczman
Positional numeration systems are a large family of numeration systems used to represent natural numbers. Whether the set of all representations forms a regular language or not is…
math.NT2022
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…