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arXiv · 1303.0969

Enumerating Abelian Returns to Prefixes of Sturmian Words

Zuzana Masáková·Edita Pelantová
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Abstract

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 $\mathcal{APR}_u$ of abelian returns of all prefixes of a Sturmian word $u$ 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 $\mathcal{APR}_u$ and we determine it for the characteristic Sturmian words.

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Zuzana Masáková, Edita Pelantová. 2013-03-05. Enumerating Abelian Returns to Prefixes of Sturmian Words. https://arxiv.org/abs/1303.0969

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