Logarithmic frequency in morphic sequences
Journal de Théorie des Nombres de Bordeaux, Tome 20 (2008) no. 2, pp. 227-241.

Nous répondons affirmativement à une question d’Allouche et Shallit en montrant l’existence de la fréquence logarithmique des lettres et des mots dans une suite morphique.

We study the logarithmic frequency of letters and words in morphic sequences and show that this frequency must always exist, answering a question of Allouche and Shallit.

DOI : https://doi.org/10.5802/jtnb.625
Classification : 68R15,  68Q45,  11B85
Mots clés : Logarithmic frequency, morphic sequences, automatic sequences
@article{JTNB_2008__20_2_227_0,
     author = {Bell, Jason P.},
     title = {Logarithmic frequency in morphic sequences},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {227--241},
     publisher = {Universit\'e Bordeaux 1},
     volume = {20},
     number = {2},
     year = {2008},
     doi = {10.5802/jtnb.625},
     mrnumber = {2477502},
     zbl = {1163.11020},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/jtnb.625/}
}
TY  - JOUR
AU  - Bell, Jason P.
TI  - Logarithmic frequency in morphic sequences
JO  - Journal de Théorie des Nombres de Bordeaux
PY  - 2008
DA  - 2008///
SP  - 227
EP  - 241
VL  - 20
IS  - 2
PB  - Université Bordeaux 1
UR  - http://www.numdam.org/articles/10.5802/jtnb.625/
UR  - https://www.ams.org/mathscinet-getitem?mr=2477502
UR  - https://zbmath.org/?q=an%3A1163.11020
UR  - https://doi.org/10.5802/jtnb.625
DO  - 10.5802/jtnb.625
LA  - en
ID  - JTNB_2008__20_2_227_0
ER  - 
Bell, Jason P. Logarithmic frequency in morphic sequences. Journal de Théorie des Nombres de Bordeaux, Tome 20 (2008) no. 2, pp. 227-241. doi : 10.5802/jtnb.625. http://www.numdam.org/articles/10.5802/jtnb.625/

[1] J.-P. Allouche, J. Shallit, Automatic Sequences: Theory, Applications, Generalizations. Cambridge University Press, Cambridge, 2003. | MR 1997038 | Zbl 1086.11015

[2] A. Cobham, Uniform tag sequences. Math. Systems Theory. 6 (1972), 164–192. | MR 457011 | Zbl 0253.02029

[3] P. Michel, Sur les ensembles minimaux engendrés par les substitutions de longueur non constante. Thèse, Université de Rennes, 1975.

[4] P. Michel, Stricte ergodicité dÕensembles minimaux de substitution. Théorie Ergodique: Actes des Journées Ergodiques, Rennes, 1973/1974, Lecture Notes in Mathematics 532, Springer-Verlag, 1976. | MR 480942 | Zbl 0331.54036

[5] S. Nicolay, M. Rigo, About frequencies of letters in generalized automatic sequences. Theoret. Comput. Sci. 374 (2007), no. 1-3, 25–40. | MR 2317465 | Zbl 1162.68032

[6] K. Saari, On the frequency of letters in morphic sequences. Computer science—theory and applications, 334–345, Lecture Notes in Comput. Sci. 3967, Springer, Berlin, 2006. | MR 2261007 | Zbl 1185.68398

[7] K. Saari, On the frequency and periodicity of infinite words. PhD thesis, University of Turku, 2008.

Cité par Sources :