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

Baláži, Peter; Masáková, Zuzana; Pelantová, Edita

Integers 5, No. 1, Paper A14, 23 p. (2005).

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

Keywords:

substitution invariant inhomogeneous bi-directional pointed Sturmian sequences; Sturmian words

Citations:

Zbl 0971.11007