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.
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.
Keywords: Logarithmic frequency, morphic sequences, automatic sequences
Bell, Jason P. 1
@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},
year = {2008},
publisher = {Universit\'e Bordeaux 1},
volume = {20},
number = {2},
doi = {10.5802/jtnb.625},
zbl = {1163.11020},
mrnumber = {2477502},
language = {en},
url = {https://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 SP - 227 EP - 241 VL - 20 IS - 2 PB - Université Bordeaux 1 UR - https://www.numdam.org/articles/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
[1] J.-P. Allouche, J. Shallit, Automatic Sequences: Theory, Applications, Generalizations. Cambridge University Press, Cambridge, 2003. | Zbl | MR
[2] A. Cobham, Uniform tag sequences. Math. Systems Theory. 6 (1972), 164–192. | Zbl | MR
[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. | Zbl | MR
[5] S. Nicolay, M. Rigo, About frequencies of letters in generalized automatic sequences. Theoret. Comput. Sci. 374 (2007), no. 1-3, 25–40. | MR | Zbl
[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 | Zbl
[7] K. Saari, On the frequency and periodicity of infinite words. PhD thesis, University of Turku, 2008.
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