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Theory of Computing Systems

, Volume 59, Issue 2, pp 161–179 | Cite as

Weak Abelian Periodicity of Infinite Words

  • Sergey Avgustinovich
  • Svetlana Puzynina
Article

Abstract

An infinite word is called weak abelian periodic if it can be represented as an infinite concatenation of finite words with identical frequencies of letters. In the paper we undertake a general study of the weak abelian periodicity property. We consider its relation with the notions of balance and letter frequency, and study operations preserving weak abelian periodicity. We establish necessary and sufficient conditions for the weak abelian periodicity of fixed points of uniform binary morphisms. Finally, we discuss weak abelian periodicity in minimal subshifts.

Keywords

Infinite word Abelian equivalence Periodicity Letter frequency Fixed points of morphisms Subshifts 

Notes

Acknowledgments

Supported in part by the Academy of Finland under grant 251371 and by the LABEX MILYON (ANR-10-LABX-0070) of Universit´e de Lyon, within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR).

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.LIP, École Normale Supérieure de LyonUniversité de LyonLyonFrance

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