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Circular Words Avoiding Patterns

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Developments in Language Theory (DLT 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2450))

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Abstract

We introduce the study of circular words avoiding patterns. We prove that there are circular binary cube-free words of every length and present several open problems regarding circular words avoiding more general patterns.

The author’s research was supported by an NSERC operating grant.

The author’s research was supported by an NSERC Undergraduate Research Award.

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References

  1. Kirby A. Baker, George. F. McNulty & Walter Taylor, Growth problems for avoidable words, Theoret. Comput. Sci. 69 (1989), no. 3, 319–345; MR 91f:68109.

    Article  MATH  MathSciNet  Google Scholar 

  2. Dwight R. Bean, Andrzej Ehrenfeucht & George McNulty, Avoidable Patterns in Strings of Symbols, Pacific J. Math. 85 (1979), 261–294.

    MATH  MathSciNet  Google Scholar 

  3. James D. Currie, There are ternary circular square-free words of length n for n ≥ 18, Elec. J. Comb. 9(1) N10.

    Google Scholar 

  4. Françoise Dejean, Sur un théorème de Thue, J. Combin. Theory Ser. A 13 (1972), 90–99.

    Article  MATH  MathSciNet  Google Scholar 

  5. Paul Erdös, Some unsolved problems, Magyar Tud. Akad. Mat. Kutato. Int. Kozl. 6 (1961), 221–254.

    MATH  Google Scholar 

  6. Earl D. Fife, Binary sequences which contain no BBb, Trans. Amer. Math. Soc. 261 (1980), 115–136; MR 82a:05034

    Article  MATH  MathSciNet  Google Scholar 

  7. Vaclav Linek, Personal communication.

    Google Scholar 

  8. Marston Morse & Gustav A. Hedlund, Symbolic dynamics I, II, Amer. J. Math. 60 (1938), 815–866; 62 (1940), 1-42; MR 1, 123d.

    Article  MATH  MathSciNet  Google Scholar 

  9. Axel Thue, Über unendliche Zeichenreihen, Norske Vid. Selsk. Skr. I. Mat. Nat. Kl. Christiana (1912), 1–67.

    Google Scholar 

  10. A. Zimin, Blocking sets of terms, Mat. Sb. (N.S.) 119 (161) (1982); Math. USSR Sbornik 47 (1984), 353-364.

    Google Scholar 

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© 2003 Springer-Verlag Berlin Heidelberg

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Currie, J.D., Fitzpatrick, D.S. (2003). Circular Words Avoiding Patterns. In: Ito, M., Toyama, M. (eds) Developments in Language Theory. DLT 2002. Lecture Notes in Computer Science, vol 2450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45005-X_28

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  • DOI: https://doi.org/10.1007/3-540-45005-X_28

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40431-6

  • Online ISBN: 978-3-540-45005-4

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