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Powers in a class of Astrict standard episturmian words, Theoret
 Comput. Sci
"... This paper concerns a specific class of strict standard episturmian words whose directive words resemble those of characteristic Sturmian words. In particular, we explicitly determine all integer powers occurring in such infinite words, extending recent results of Damanik and Lenz (2003), who studie ..."
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Cited by 10 (8 self)
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This paper concerns a specific class of strict standard episturmian words whose directive words resemble those of characteristic Sturmian words. In particular, we explicitly determine all integer powers occurring in such infinite words, extending recent results of Damanik and Lenz (2003), who studied powers in Sturmian words. The key tools in our analysis are canonical decompositions and a generalization of singular words, which were originally defined for the ubiquitous Fibonacci word. Our main results are demonstrated via some examples, including the kbonacci word, a generalization of the Fibonacci word to a kletter alphabet (k≥2).
Episturmian words: a survey
, 2007
"... In this paper, we survey the rich theory of infinite episturmian words which generalize to any finite alphabet, in a rather resembling way, the wellknown family of Sturmian words on two letters. After recalling definitions and basic properties, we consider episturmian morphisms that allow for a dee ..."
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Cited by 7 (1 self)
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In this paper, we survey the rich theory of infinite episturmian words which generalize to any finite alphabet, in a rather resembling way, the wellknown family of Sturmian words on two letters. After recalling definitions and basic properties, we consider episturmian morphisms that allow for a deeper study of these words. Some properties of factors are described, including factor complexity, palindromes, fractional powers, frequencies, and return words. We also consider lexicographical properties of episturmian words, as well as their connection to the balance property, and related notions such as finite episturmian words, ArnouxRauzy sequences, and “episkew words ” that generalize the skew words of Morse and Hedlund. Keywords: combinatorics on words; episturmian words; ArnouxRauzy sequences; Sturmian words; episturmian morphisms. MSC (2000): 68R15. 1
Directive words of episturmian words: equivalences and normalization
, 2008
"... Episturmian morphisms constitute a powerful tool to study episturmian words. Indeed, any episturmian word can be infinitely decomposed over the set of pure episturmian morphisms. Thus, an episturmian word can be defined by one of its morphic decompositions or, equivalently, by a certain directive wo ..."
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Cited by 3 (3 self)
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Episturmian morphisms constitute a powerful tool to study episturmian words. Indeed, any episturmian word can be infinitely decomposed over the set of pure episturmian morphisms. Thus, an episturmian word can be defined by one of its morphic decompositions or, equivalently, by a certain directive word. Here we characterize pairs of words directing a common episturmian word. We also propose a way to uniquely define any episturmian word through a normalization of its directive words. As a consequence of these results, we characterize episturmian words having a unique directive word. Keywords: episturmian word; Sturmian word; ArnouxRauzy sequence; episturmian morphism; directive word. MSC (2000): 68R15. 1
On θepisturmian words
, 2008
"... In this paper we study a class of infinite words on a finite alphabet A whose factors are closed under the image of an involutory antimorphism θ of the free monoid A ∗. We show that given a recurrent infinite word ω ∈ A N, if there exists a positive integer K such that for each n ≥ 1 the word ω has ..."
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In this paper we study a class of infinite words on a finite alphabet A whose factors are closed under the image of an involutory antimorphism θ of the free monoid A ∗. We show that given a recurrent infinite word ω ∈ A N, if there exists a positive integer K such that for each n ≥ 1 the word ω has 1) card A + (n − 1)K distinct factors of length n, and 2) a unique right and a unique left special factor of length n, then there exists an involutory antimorphism θ of the free monoid A∗ preserving the set of factors of ω.