Language structure of pattern Sturmian words

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Language structure of pattern Sturmian words

Pattern Sturmian words introduced by Kamae and Zamboni KZ KZ are an analogy of Sturmian words for the maximal pattern com plexity instead of the block complexity So far two kinds of recur rent pattern Sturmian words are known namely rotation words and Toeplitz words But neither a structural characterization nor a reason able classi cation of the recurrent pattern Sturmian words is known In this...

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On the Structure of Bispecial Sturmian Words

A balanced word is one in which any two factors of the same length contain the same number of each letter of the alphabet up to one. Finite binary balanced words are called Sturmian words. A Sturmian word is bispecial if it can be extended to the left and to the right with both letters remaining a Sturmian word. There is a deep relation between bispecial Sturmian words and Christoffel words, th...

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Palindromes in Sturmian Words

We study some structural and combinatorial properties of Sturmian palindromes, i.e., palindromic finite factors of Sturmian words. In particular, we give a formula which permits to compute in an exact way the number of Sturmian palindromes of any length. Moreover, an interesting characterization of Sturmian palindromes is obtained.

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On the Structure of Bispecial Sturmian Words I

A balanced word is one in which any two factors of the same length contain the same number of each letter of the alphabet up to one. Finite binary balanced words are called Sturmian words. A Sturmian word is bispecial if it can be extended to the left and to the right with both letters remaining a Sturmian word. There is a deep relation between bispecial Sturmian words and Christoffel words, th...

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Return words in Sturmian and episturmian words

Considering each occurrence of a word w in a recurrent infinite word, we define the set of return words of w to be the set of all distinct words beginning with an occurrence of w and ending exactly just before the next occurrence of w in the infinite word. We give a simpler proof of the recent result (of the second author) that an infinite word is Sturmian if and only if each of its factors has...

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ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 2006

ISSN: 0012-365X

DOI: 10.1016/j.disc.2006.03.043