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Factor Complexity of Infinite Words Associated with Non-Simple Parry Numbers

Karel Klouda
  • FNSPE, Czech Technical University, Prague, Czech Republic, and LIAFA, Université Denis-Diderot (Paris VII), France. E-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Edita Pelantová
  • FNSPE, Czech Technical University, Prague, Czech Republic, and Doppler Institute for Mathematical Physics and Applied Mathematics, Prague, Czech Republic. E-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2009-08-20 | DOI: https://doi.org/10.1515/INTEG.2009.025

Abstract

The factor complexity of the infinite word u β canonically associated with a non-simple Parry number β is studied. Our approach is based on the notion of special factors introduced by Berstel and Cassaigne. At first, we give a handy method for determining infinite left special branches; this method is applicable to a broad class of infinite words which are fixed points of a primitive substitution. In the second part of the article, we focus on infinite words u β only. To complete the description of their special factors, we define and study (a, b)-maximal left special factors. This enables us to characterize non-simple Parry numbers β for which the word u β has affine complexity.

Keywords.: Factor complexity function; Parry numbers

About the article

Received: 2008-10-31

Accepted: 2009-02-13

Published Online: 2009-08-20

Published in Print: 2009-08-01


Citation Information: Integers, Volume 9, Issue 3, Pages 281–309, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/INTEG.2009.025.

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