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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.CO2025
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…
math.CO2025
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…