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
Infinite Words with very Low Factor Complexity: an introduction to Combinatorics on Words
Mélodie Andrieu
These lecture notes provide an introduction to combinatorics on words and its interactions with dynamics, algebra, and arithmetic. The central theme is the notion of low factor com…