5 papers
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…
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…
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…
A Rauzy fractal unbounded in all directions of the plane
Mélodie Andrieu
We construct an Arnoux-Rauzy word for which the set of all differences of two abelianized factors is equal to . In particular, the imbalance of this word is infinite…
Morphic words and equidistributed sequences
Mélodie Andrieu, Anna E. Frid
The problem we consider is the following: Given an infinite word on an ordered alphabet, construct the sequence , equidistributed on and such that $ν[m]<ν…