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More on morphisms and almost-periodicity

✍ Scribed by Arnaud Maes

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 143 KB
Volume: 231
Category: Article
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(99)00101-2

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In 1965, Fine and Wilf proved the following theorem: if (fn)n¿0 and (gn)n¿0 are periodic sequences of real numbers, of period lengths h and k, respectively, and fn = gn for 0 6 n ¡ h + k -gcd(h; k), then fn = gn for all n ¿ 0. Furthermore, the constant h + k -gcd(h; k) is best possible. In this pape

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We consider so-called Toeplitz words which can be viewed as generalizations of one-way infinite periodic words . We compute their subword complexity , and show that they can always be generated by iterating periodically a finite number of morphisms . Moreover , we define a structural classification