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Sequences of low arithmetical complexity

Published online by Cambridge University Press:  08 November 2006

Sergey V. Avgustinovich ,
Julien Cassaigne  and
Anna E. Frid
Sergey V. Avgustinovich
Affiliation:
Sobolev Institute of Mathematics SB RAS, Koptyug Av. 4, Novosibirsk, Russia; avgust@math.nsc.ru; frid@math.nsc.ru
Julien Cassaigne
Affiliation:
Institut de Mathématiques de Luminy, case 907, 163 Av. de Luminy, 13288 Marseille Cedex 9, France; cassaigne@iml.univ-mrs.fr
Anna E. Frid
Affiliation:
Sobolev Institute of Mathematics SB RAS, Koptyug Av. 4, Novosibirsk, Russia; avgust@math.nsc.ru; frid@math.nsc.ru
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Abstract

Arithmetical complexity of a sequence is the number of words of length n that can be extracted from it according to arithmetic progressions. We study uniformly recurrent words of low arithmetical complexity and describe the family of such words having lowest complexity.

Keywords

Arithmetical complexityinfinite wordsToeplitz wordsspecial factorsperiod doubling wordLegendre symbolpaperfolding word.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 40 , Issue 4 , October 2006 , pp. 569 - 582
Copyright
© EDP Sciences, 2006

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