On the Index of Sturmian Words
نویسنده
چکیده
An innnite word x has nite index if the exponents of the powers of primitive words that are factors of x are bounded. F. Mignosi has proved that a Sturmian word has nite index if and only if the coeecients of the continued fraction development of its slope are bounded. Mignosi's proof relies on a delicate analysis of the approximation of the slope by rational numbers. We give here a proof based on combinatorial properties of words, and give some additional relations between the exponents and the slope.
منابع مشابه
Characterization of Repetitions in Sturmian Words: A New Proof
We present a new, dynamical way to study powers (or repetitions) in Sturmian words based on results from Diophantine approximation theory. As a result, we provide an alternative and shorter proof of a result by Damanik and Lenz characterizing powers in Sturmian words [Powers in Sturmian Sequences, European J. Combin. 24 (2003), 377–390]. Further, as a consequence, we obtain a previously known f...
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 کاملRelation 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 کاملBifix codes and Sturmian words
We study bifix codes in factorial sets of words. We generalize most properties of ordinary maximal bifix codes to bifix codes maximal in a recurrent set F of words (F -maximal bifix codes). In the case of bifix codes contained in Sturmian sets of words, we obtain several new results. Let F be a Sturmian set of words. Our results express the fact that an F -maximal bifix code of degree d behaves...
متن کاملSturmian and Episturmian Words (A Survey of Some Recent Results)
This survey paper contains a description of some recent results concerning Sturmian and episturmian words, with particular emphasis on central words. We list fourteen characterizations of central words. We give the characterizations of Sturmian and episturmian words by lexicographic ordering, we show how the Burrows-Wheeler transform behaves on Sturmian words. We mention results on balanced epi...
متن کامل