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Enumerating Abelian Returns to Prefixes of Sturmian Words
We follow the works of Puzynina and Zamboni, and Rigo et al. on abelian
returns in Sturmian words. We determine the cardinality of the set
of abelian returns of all prefixes of a Sturmian word in
terms of the coefficients of the continued fraction of the slope, dependingly
on the intercept. We provide a simple algorithm for finding the set
and we determine it for the characteristic Sturmian words.Comment: 19page