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A word of low complexity without uniform frequencies

Part of: Ergodic theory Topological dynamics Discrete mathematics in relation to computer science

Published online by Cambridge University Press:  29 May 2023

JULIEN CASSAIGNE  and
IDRISSA KABORÉ Open the ORCID record for IDRISSA KABORÉ [Opens in a new window]
JULIEN CASSAIGNE
Affiliation:
Institut de Mathématiques de Marseille, 163 avenue de Luminy, case 907, F-13288 Marseille Cedex 9, France (e-mail: [email protected])
IDRISSA KABORÉ*
Affiliation:
UFR-Sciences Exactes et Appliquées, Université Nazi Boni, 01 BP 1091 Bobo-Dioulasso 01, Burkina Faso
*
e-mail: [email protected]
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Abstract

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.

Keywords

infinite wordsubstitutioncomplexityuniform frequencies

MSC classification

Primary: 37B10: Symbolic dynamics 37A25: Ergodicity, mixing, rates of mixing 68R15: Combinatorics on words
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 44 , Issue 4 , April 2024 , pp. 1013 - 1025
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

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