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Interval Exchange Words and the Question of Hof, Knill, and Simon

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Developments in Language Theory (DLT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9168))

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Abstract

We consider words coding non-degenerate 3 interval exchange transformation. It is known that such words contain infinitely many palindromic factors. We show that for any morphism \(\xi \) fixing such a word, either \(\xi \) or \(\xi ^2\) is conjugate to a class P morphism. By this, we provide a new family of palindromic infinite words satisfying the conjecture of Hof, Knill and Simon, as formulated by Tan.

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References

  1. Arnoux, P., Berthé, V., Masáková, Z., Pelantová, E.: Sturm numbers and substitution invariance of 3iet words. Integers 8 (Article A14) (2008)

    Google Scholar 

  2. Blondin Massé, A., Brlek, S., Garon, A., Labbé, S.: Equations on palindromes and circular words. Theoret. Comput. Sci. 412, 2922–2930 (2011)

    Article  MathSciNet  Google Scholar 

  3. Blondin Massé, A., Brlek, S., Labbé, S.: Palindromic lacunas of the Thue-Morse word. In: Proc. GASCom 2008, pp. 53–67 (2008)

    Google Scholar 

  4. Ferenczi, S., Holton, C., Zamboni, L.: Structure of three-interval exchange transformations II: a combinatorial description of the tranjectories. J. Anal. Math. 89, 239–276 (2003)

    Article  MathSciNet  Google Scholar 

  5. Gawrychowski, P., Manea, F., Nowotka, D.: Testing generalised freeness of words. In: Mayr, E.W., Portier, N. (eds.) 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). (LIPIcs), vol. 25, pp. 337–349. Dagstuhl, Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Germany (2014)

    Google Scholar 

  6. Hof, A., Knill, O., Simon, B.: Singular continuous spectrum for palindromic Schrödinger operators. Comm. Math. Phys. 174, 149–159 (1995)

    Article  MathSciNet  Google Scholar 

  7. Kari, L., Mahalingam, K.: Watson-crick conjugate and commutative words. In: Garzon, M.H., Yan, H. (eds.) DNA 2007. LNCS, vol. 4848, pp. 273–283. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  8. Keane, M.: Interval exchange transformations. Math. Z. 141, 25–31 (1975)

    Article  MathSciNet  Google Scholar 

  9. Labbé, S., Pelantová, E.: Palindromic sequences generated from marked morphisms. Eur. J. Comb. 51, 200–214 (2016)

    Article  Google Scholar 

  10. Labbé, S.: A counterexample to a question of Hof, Knill and Simon. Electron. J. Comb. 21 (2014)

    Google Scholar 

  11. Lothaire, M.: Algebraic combinatorics on words. Encyclopedia of Mathematics and its Applications, vol. 90. Cambridge University Press (2002)

    Google Scholar 

  12. Masáková, Z., Pelantová, E., Starosta, Š: Interval exchange words and the question of Hof, Knill, and Simon (2015). (preprint available at) http://arxiv.org/abs/1503.03376

  13. Tan, B.: Mirror substitutions and palindromic sequences. Theoret. Comput. Sci. 389, 118–124 (2007)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00, Praha 2, Czech Republic

    Zuzana Masáková & Edita Pelantová

  2. Faculty of Information Technology, Czech Technical University in Prague, Thákurova 9, 160 00, Praha 6, Czech Republic

    Štěpán Starosta

Authors
  1. Zuzana Masáková
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  2. Edita Pelantová
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  3. Štěpán Starosta
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Corresponding author

Correspondence to Štěpán Starosta .

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Editors and Affiliations

  1. University of Liverpool, Liverpool, United Kingdom

    Igor Potapov

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Masáková, Z., Pelantová, E., Starosta, Š. (2015). Interval Exchange Words and the Question of Hof, Knill, and Simon. In: Potapov, I. (eds) Developments in Language Theory. DLT 2015. Lecture Notes in Computer Science(), vol 9168. Springer, Cham. https://doi.org/10.1007/978-3-319-21500-6_30

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  • DOI: https://doi.org/10.1007/978-3-319-21500-6_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21499-3

  • Online ISBN: 978-3-319-21500-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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