Logarithmic frequency in morphic sequences. (English) Zbl 1163.11020

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.


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