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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.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…