Relation between powers of factors and the recurrence function characterizing Sturmian words
نویسندگان
چکیده
منابع مشابه
Relation between powers of factors and the recurrence function characterizing Sturmian words
In this paper we put into relation the index of an infinite aperiodic word and its recurrence function. With the use of this relation, we then give a new characterization of Sturmian words. As a byproduct, we give a new proof of theorem of Damanik and Lenz describing the index of a Sturmian word in terms of the continued fraction expansion of its slope.
متن کاملRelation between powers of factors and recurrence function characterizing Sturmian words
In this paper we put into relation the index of an infinite aperiodic word and its recurrence function. With the use of this relation, we then give a new characterization of Sturmian words. As a byproduct, we give a new proof of theorem of Damanik and Lenz describing the index of a Sturmian word in terms of the continued fraction expansion of its slope.
متن کاملAbelian powers and repetitions in Sturmian words
Richomme, Saari and Zamboni (J. Lond. Math. Soc. 83: 79–95, 2011) proved that at every position of an infinite Sturmian word starts an abelian power of exponent k, for every positive integer k. Here, we improve on this result, studying the maximal exponent of abelian powers and abelian repetitions (an abelian repetition is the analogous of a fractional power in the abelian setting) occurring in...
متن کاملStandard Words and Abelian Powers in Sturmian Words
We give three descriptions of the factors of a Sturmian word that are standard words. We also show that all Sturmian words are so-called everywhere abelian krepetitive for all integers k ≥ 1, that is, all sufficiently long factors have an abelian kth power as a prefix. More precisely, given a Sturmian word t and an integer k, there exist two integers `1 and `2 such that each position in t has a...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2009
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2009.04.003