6 papers
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…
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…
On two conjectures of Shallit about Thue-Morse-like sequences
Lubomíra Dvořáková, Savinien Kreczman, Edita Pelantová
We study a class of infinite words , where is a positive integer, recently introduced by J. Shallit. This class includes the Thue-Morse sequence , the Fibonacci-Thue…
Positionality of Dumont--Thomas numeration systems for integers
Savinien Kreczman, Sébastien Labbé, Manon Stipulanti
Introduced in 2001 by Lecomte and Rigo, abstract numeration systems provide a way of expressing natural numbers with words from a language accepted by a finite automaton. As it…
Magic numbers in periodic sequences
Savinien Kreczman, Luca Prigioniero, Eric Rowland +1
In formal languages and automata theory, the magic number problem can be formulated as follows: for a given integer n, is it possible to find a number d in the range [n,2^n] such t…
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…