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On defect effect of bi-infinite words

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Mathematical Foundations of Computer Science 1998 (MFCS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1450))

Abstract

We prove the following two variants of the defect theorem. Let X be a finite set of words over a finite alphabet. Then if a nonperiodic bi-infinite word w has two X-factorizations, then the combinatorial rank of X is at most card(X) - 1, i.e. there exists a set F such that \(X \subseteq F^ + \) with card(F) < card(X). Further, if card(X)=2 and a bi-infinite word possesses two X-factorizations which are not shift-equivalent, then the primitive roots of the words in X are conjugates. Moreover, in the case card(F)=card(X), the number of periodic bi-infinite words which have two different X-factorizations is finite and in the two-element case there is at most one such bi-infinite word.

Supported by Academy of Finland under Grant No. 14047.

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References

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Authors and Affiliations

  1. Department of Mathematics and Turku Centre for Computer Science, University of Turku, SF-20014, Turku, Finland

    Juhani Karhumäki, Ján Maňuch & Wojciech Plandowski

Authors
  1. Juhani Karhumäki
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  2. Ján Maňuch
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  3. Wojciech Plandowski
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Luboš Brim Jozef Gruska Jiří Zlatuška

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© 1998 Springer-Verlag Berlin Heidelberg

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Karhumäki, J., Maňuch, J., Plandowski, W. (1998). On defect effect of bi-infinite words. In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055818

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  • DOI: https://doi.org/10.1007/BFb0055818

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64827-7

  • Online ISBN: 978-3-540-68532-6

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