Logarithmic frequency in morphic sequences
Journal de théorie des nombres de Bordeaux, Volume 20 (2008) no. 2, pp. 227-241.

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.

DOI: 10.5802/jtnb.625
Classification: 68R15, 68Q45, 11B85
Mots-clés : Logarithmic frequency, morphic sequences, automatic sequences

Jason P. Bell 1

1 Department of Mathematics Simon Fraser University Burnaby, BC, V5A 1S6, CANADA
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Jason P. Bell. Logarithmic frequency in morphic sequences. Journal de théorie des nombres de Bordeaux, Volume 20 (2008) no. 2, pp. 227-241. doi : 10.5802/jtnb.625. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.625/

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

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

[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 | Zbl

[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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