Combinatorial and Arithmetical Properties of Linear Numeration Systems

Dedicated to the memory of Paul Erdős

We extend a result of J. Alexander and D. Zagier on the Garsia entropy of the Erdős measure. Our investigation heavily relies on methods from combinatorics on words. Furthermore, we introduce a new singular measure related to the Farey tree.

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Received October 7, 1999

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ID="†" This author is supported by the START-project Y96-MAT of the Austrian Science Fund

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ID="‡" This author is supported by the Austrian Science Fund (FWF) grant P14200-MAT

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ID="*" This author is supported by the Austrian Science Fund (FWF) grant S8307-MAT

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Grabner, P., Kirschenhofer, P. & Tichy, R. Combinatorial and Arithmetical Properties of Linear Numeration Systems. Combinatorica 22, 245–267 (2002). https://doi.org/10.1007/s004930200011

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  • AMS Subject Classification (2000) Classes:  11K55; 05A17, 11A63, 28D20