3 papers
math.CO2026
A proof of Rauzy's conjecture on abelian complexity
Mélodie Andrieu, Léo Vivion
We resolve a conjecture posed by Rauzy in 1983 concerning the -ary generalizations of Sturmian words. A classical theorem by Coven and Hedlund from 1973 states that Sturmian wor…
math.NT2026
A Normality Conjecture on Rational Base Number Systems
Mélodie Andrieu, Shalom Eliahou, Léo Vivion
The rational base number system, introduced by Akiyama, Frougny, and Sakarovitch in 2008, is a generalization of the classical integer base number system. Within this framework two…
math.CO2026
New examples of words for which binomial complexities and subword complexity coincide
Léo Vivion
The complexity of an infinite word can be measured in several ways, the two most common measures being the subword complexity and the abelian complexity. In 2015, Rigo and Salimov…