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Borel, J.-P.; Laubie, F.

Certain words on the real projective line. (Quelques mots sur la droite projective réelle.) (French) Zbl 0839.11008

J. Théor. Nombres Bordx. 5, No. 1, 23-51 (1993).
The authors give complete proofs of their results announced in [C. R. Acad. Sci., Paris, Sér. I 313, 483-485 (1991; Zbl 0742.11013)] and F. Laubie [ibid. 565-567 (1991; Zbl 0768.11024)]. This is a pleasant paper playing with words, namely Christoffel and Lyndon words. They link substitutions acting on infinite Christoffel words with the action of \(\text{SL}_2 (\mathbb{Z})\) on the projective real line.
Reviewer: P.Liardet (Marseille)

Cited in 1 Review
Cited in 57 Documents

MSC:

11B85 Automata sequences
68R15 Combinatorics on words
11A55 Continued fractions
11A67 Other number representations

Keywords:

combinatorics on words; Lyndon word; homography; substitutions; infinite Christoffel words

Citations:

Zbl 0742.11013; Zbl 0768.11024
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\textit{J. P. Borel} and \textit{F. Laubie}, J. Théor. Nombres Bordx. 5, No. 1, 23--51 (1993; Zbl 0839.11008)
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