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Combinatorics of Three-Interval Exchanges

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Book cover Automata, Languages and Programming (ICALP 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2076))

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Abstract

We generalize the interaction between Sturmian infinite words and rotations of the 1-dimensional torus by giving a set of necessary and sufficient conditions for a language to be a natural coding of a three-interval exchange. This solves an old question of Rauzy, and allows us to give a complete combinatorial description of such languages through an algorithm of simultaneous approximation.

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Author information

Authors and Affiliations

  1. Institut de Mathématiques de Luminy, CNRS - UPR 9016, Case 907, 163 av. de Luminy, F13288, Marseille Cedex 9, France

    Sébastien Ferenczi

  2. Department of Mathematics, University of California, Berkeley, CA, 94720-3840, USA

    Charles Holton

  3. Department of Mathematics, University of North Texas, Denton, TX, 76203-5116, USA

    Luca Q. Zamboni

Authors
  1. Sébastien Ferenczi
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  2. Charles Holton
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  3. Luca Q. Zamboni
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Editor information

Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informátics, Univ. Politècnica de Catalunya, C/Jordi Girona Salgado 1-3, 08034, Barcelona, Spain

    Fernando Orejas

  2. Computer Technology Institute (CTI), University of Patras, 61 Riga Feraiou street, 26221, Patras, Greece

    Paul G. Spirakis

  3. Institute of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584, CH, Utrecht, The Netherlands

    Jan van Leeuwen

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© 2001 Springer-Verlag Berlin Heidelberg

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Ferenczi, S., Holton, C., Zamboni, L.Q. (2001). Combinatorics of Three-Interval Exchanges. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_47

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  • DOI: https://doi.org/10.1007/3-540-48224-5_47

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42287-7

  • Online ISBN: 978-3-540-48224-6

  • eBook Packages: Springer Book Archive

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