A Proof of Rauzy's Conjecture on Abelian Complexity
Combinatorics
2026-05-05 v1 Dynamical Systems
Abstract
A celebrated theorem by Coven and Hedlund (1973) states that Sturmian words are characterized by their abelian complexity: they are precisely the infinite words with rationally independent letter frequencies and constant abelian complexity equal to 2. In this article, we prove a conjecture of Rauzy (1983), showing that there do not exist infinite ternary words with rationally independent letter frequencies and constant abelian complexity equal to 3.
Keywords
Cite
@article{arxiv.2605.01577,
title = {A Proof of Rauzy's Conjecture on Abelian Complexity},
author = {Mélodie Andrieu and Léo Vivion},
journal= {arXiv preprint arXiv:2605.01577},
year = {2026}
}