Enumerating Abelian Returns to Prefixes of Sturmian Words

2013/03/05 by Zuzana Masáková, Edita Pelantová, Masáková, Zuzana +1
Computer Science · Mathematics · #Authorship Attribution and Profiling #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Natural Language Processing Techniques #cs.FL #math.CO #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1303.0969

19pages

arxiv created 2013/03/05 · openalex publication_date 2013/03/05 · arxiv updated 2013/03/06 · openalex created_date 2022/09/18 · openalex updated_date 2026/07/28

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 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 APR_u and we determine it for the characteristic Sturmian words.

Related

• Abelian returns in Sturmian words
• Relation between powers of factors and recurrence function characterizing Sturmian words
• α-numbers, diophantine exponent and factorisations of sturmian words
• Combinatorial structure of Sturmian words and continued fraction expansions of Sturmian numbers
• Abelian Powers and Repetitions in Sturmian Words