Languages under substitutions and balanced words
Journal de Théorie des Nombres de Bordeaux, Tome 16 (2004) no. 1, pp. 151-172.

Cet article est constitué de trois parties. Dans la première on prouve un théorème général sur l’image d’un language K sous une subsitution. Dans la seconde on applique ce théorème au cas spécial prenant pour K le language des mots balancés et la troisième partie concerne les mots bi-infinis récurrents de croissance de complexité minimale (“minimal block growth”).

This paper consists of three parts. In the first part we prove a general theorem on the image of a language K under a substitution, in the second we apply this to the special case when K is the language of balanced words and in the third part we deal with recurrent Z-words of minimal block growth.

@article{JTNB_2004__16_1_151_0,
     author = {Alex Heinis},
     title = {Languages under substitutions and balanced words},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {151--172},
     publisher = {Universit\'e Bordeaux 1},
     volume = {16},
     number = {1},
     year = {2004},
     doi = {10.5802/jtnb.438},
     mrnumber = {2145577},
     zbl = {02184636},
     language = {en},
     url = {jtnb.centre-mersenne.org/item/JTNB_2004__16_1_151_0/}
}
Alex Heinis. Languages under substitutions and balanced words. Journal de Théorie des Nombres de Bordeaux, Tome 16 (2004) no. 1, pp. 151-172. doi : 10.5802/jtnb.438. https://jtnb.centre-mersenne.org/item/JTNB_2004__16_1_151_0/

[Be/Po] J. Berstel, M. Pocchiola, A geometric proof of the enumeration formula for Sturmian words. Internat. J. Algebra Comput. 3 (1993), 394–355. | MR 1240390 | Zbl 0802.68099

[Ca] J. Cassaigne, Complexité et facteurs spéciaux. Bull. Belg. Math. Soc. 4 (1997), 67–88. | MR 1440670 | Zbl 0921.68065

[CH] E.M. Coven, G.A. Hedlund, Sequences With Minimal Block Growth. Math. Systems Th. 7 (1971), 138–153. | MR 322838 | Zbl 0256.54028

[dL/Mi] A. de Luca, F. Mignosi, Some combinatorial properties of Sturmian words. Theoret. Comp. Sci. 136 (1994), 361–385. | MR 1311214 | Zbl 0874.68245

[FW] N.J. Fine, H.S. Wilf, Uniqueness theorems for periodic functions. Proc. Amer. Math. Soc. 16 (1965), 109–114. | MR 174934 | Zbl 0131.30203

[H] A. Heinis, Arithmetics and combinatorics of words of low complexity. Doctor’s Thesis Rijksuniversiteit Leiden (2001). Available on | Zbl 01844170

[L] M. Lothaire, Mots. Hermès Paris 1990. | MR 1252659 | Zbl 0862.05001

[MH] M. Morse, G.A. Hedlund, Symbolic dynamics II: Sturmian trajectories. Amer. J. Math. 62 (1940), 1–42. | MR 745 | Zbl 0022.34003

[Mi] F. Mignosi, On the number of factors of Sturmian words. Theoret. Comp. Sci. 82 (1991), 71–84. | MR 1112109 | Zbl 0728.68093

[Mi/S] F. Mignosi, P. Séébold, Morphismes sturmiens et règles de Rauzy. J. Th. Nombres Bordeaux 5 (1993), 211–233. | Numdam | MR 1265903 | Zbl 0797.11029

[T] R. Tijdeman, Intertwinings of periodic sequences. Indag. Math. 9 (1998), 113–122. | MR 1618219 | Zbl 0918.11012