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uniform frequencies

Ergodic Theory and Dynamical Systems (1)

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A word of low complexity without uniform frequencies
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JULIEN CASSAIGNE, IDRISSA KABORÉ
Journal:

Ergodic Theory and Dynamical Systems / Volume 44 / Issue 4 / April 2024

Published online by Cambridge University Press:

29 May 2023, pp. 1013-1025

Print publication:

April 2024
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In this paper, we construct a uniformly recurrent infinite word of low complexity without uniform frequencies of letters. This shows the optimality of a bound of Boshernitzan, which gives a sufficient condition for a uniformly recurrent infinite word to admit uniform frequencies.