Sturmian words: structure, combinatorics, and their arithmetics

Luca, Aldo de

doi:10.1016/s0304-3975(96)00310-6

Cited by 156 publications

(168 citation statements)

References 7 publications

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“…It is well-known that overlapping palindromes yield periodicity [6,1]. One can ask what is the result of overlapping pseudopalindromes.…”

Section: Pseudoperiodicitymentioning

confidence: 99%

“…They proved that those words are exactly the maximum ones admitting two periods p and q, with gcd(p, q) = 1, but not with period 1 [8]. In [6], De Luca studied words generated by iterated palindromic closure -an operator that allows one to generate infinite words having infinitely many palindromic prefixes -and proved that central words are obtained by iterated palindromic closure. More recently, de Luca and De Luca defined a family of words called generalized pseudostandard words that are generated by iterated pseudopalindromic closure.…”

Section: Introductionmentioning

confidence: 99%

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Multipseudoperiodic Words

Massé

DESMEULES

Gaboury

et al. 2013

Int. J. Found. Comput. Sci.

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We consider words over an arbitrary alphabet admitting multiple pseudoperiods according to permutations. We describe the conditions under which such a word exists. Moreover, a natural generalization of Fine and Wilf's Theorem is proved. Finally, we introduce and describe a new family of words sharing properties with the so-called central words. In particular, under some simple conditions, we prove that these words are pseudopalindromes, a result consistent with the fact that central words are palindromes.

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“…It is well-known that overlapping palindromes yield periodicity [6,1]. One can ask what is the result of overlapping pseudopalindromes.…”

Section: Pseudoperiodicitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multipseudoperiodic Words

Massé

DESMEULES

Gaboury

et al. 2013

Int. J. Found. Comput. Sci.

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“…For instance, for u = 0100101, one gets u (+) = 01001010010. The following characterization is due to de Luca [20]. where u 0 = ε and u n+1 = (u n a n ) (+) , for n ≥ 0.…”

Section: Palindromic Closurementioning

confidence: 99%

“…Several reviews of properties of Sturmian words and related infinite words exist, by T. C. Brown [10], Berstel [4], de Luca [20], Parvaix [39]. For early work, see Venkov [44].…”

Section: Introductionmentioning

confidence: 99%

Recent Results on Extensions of Sturmian Words

Berstel

2002

Int. J. Algebra Comput.

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Sturmian words are infinite words over a two-letter alphabet that admit a great number of equivalent definitions. Most of them have been given in the past ten years. Among several extensions of Sturmian words to larger alphabets, the Arnoux-Rauzy words appear to share many of the properties of Sturmian words. In this survey, combinatorial properties of these two families are considered and compared.

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“…This word is certainly one of the most studied words in the combinatorics on words, (see, e.g., [2,6,7,9,15,22]). It is the archetype of a Sturmian word [14].…”

Section: Introductionmentioning

confidence: 99%