## Complete characterization of substitution invariant Sturmian sequences.(English)Zbl 1121.11020

Summary: We provide a complete characterization of substitution invariant inhomogeneous bidirectional pointed Sturmian sequences. The result is analogous to that obtained by V. Berthé, H. Ei, S. Ito and H. Rao [Invertible substitutions and Sturmian words: an application of Rauzy fractals”, RAIRO, Théor. Inf. Appl. 41, No. 3, 329–349 (2007), doi:10.1051/ita:2007026] and S. Yasutomi [in Kanemitsu, Shigeru (ed.) et al., Number theory and its applications. Proceedings of the conference held at the RIMS, Kyoto, Japan, 1997. Dordrecht: Kluwer Academic Publishers, Dev. Math. 2, 347–373 (1999; Zbl 0971.11007)] for one-directional Sturmian words. The proof is constructive, based on the geometric representation of Sturmian words by a cut-and-project scheme.

### MSC:

 11B85 Automata sequences 68R15 Combinatorics on words

Zbl 0971.11007
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