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Bell, Jason P.

Logarithmic frequency in morphic sequences. (English) Zbl 1163.11020

J. Théor. Nombres Bordx. 20, No. 2, 227-241 (2008).
This paper answers a question raised by [J.-P. Allouche and J. Shallit, Automatic sequences. Theory, applications, generalizations. Cambridge: Cambridge University Press (2003; Zbl 1086.11015)] by showing that the logarithmic frequency of letters appearing in a morphic sequence always exists. This extends a result of A. Cobham [Math. Syst. Theory 6, 164–192 (1972; Zbl 0253.02029)] showing that the logarithmic frequency of letters appearing in an automatic sequence always exists, while the natural frequency need not exist.
Reviewer: Thomas Ward (Norwich)

Cited in 3 Documents

MSC:

11B85 Automata sequences
37B10 Symbolic dynamics
68R15 Combinatorics on words

Keywords:

Morphic sequence; logarithmic frequency

Citations:

Zbl 1086.11015; Zbl 0253.02029
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\textit{J. P. Bell}, J. Théor. Nombres Bordx. 20, No. 2, 227--241 (2008; Zbl 1163.11020)
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References:

[1] J.-P. Allouche, J. Shallit, Automatic Sequences: Theory, Applications, Generalizations. Cambridge University Press, Cambridge, 2003. · Zbl 1086.11015
[2] A. Cobham, Uniform tag sequences. Math. Systems Theory. 6 (1972), 164-192. · 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. · 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. · 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. · Zbl 1185.68398
[7] K. Saari, On the frequency and periodicity of infinite words. PhD thesis, University of Turku, 2008.
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