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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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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