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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.CO2025
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…