Geodesic
On the conjectures of Rauzy and Shallit for infinite words
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 4, pp. 705-711.

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We show a connection between a recent conjecture of Shallit and an older conjecture of Rauzy for infinite words on a finite alphabet. More precisely we show that a Rauzy-like conjecture is equivalent to Shallit's. In passing we correct a misprint in Rauzy's conjecture.
Classification : 11B05, 11B85, 68R15
Keywords: combinatorics on words; recurrence function; Sturmian sequences 
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     author = {Allouche, Jean-Paul and Bousquet-M\'elou, Mireille},
     title = {On the conjectures of {Rauzy} and {Shallit} for infinite words},
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Allouche, Jean-Paul; Bousquet-Mélou, Mireille. On the conjectures of Rauzy and Shallit for infinite words. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 4, pp. 705-711. http://geodesic.mathdoc.fr/item/CMUC_1995__36_4_a7/