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Standard factors of Sturmian words

Published online by Cambridge University Press:  11 February 2010

Gwénaël Richomme ,
Kalle Saari  and
Luca Q. Zamboni
Gwénaël Richomme
Affiliation:
Université de Picardie Jules Verne, Laboratoire MIS (Modélisation, Information, Systèmes), 33 rue Saint Leu, 80039 Amiens Cedex 1, France; gwenael.richomme@u-picardie.fr Université Paul-Valéry Montpellier 3, UFR 4, Dpt. MIAp, Route de Mende, 34199 Montpellier Cedex 5, gwenael.richomme@univ-montp3.fr
Kalle Saari
Affiliation:
Department of Mathematics and Turku Centre for Computer Science, University of Turku, 20014 Turku, Finland; kasaar@utu.fi
Luca Q. Zamboni
Affiliation:
Université de Lyon, Université Lyon 1, CNRS UMR 5208 Institut Camille Jordan, Bâtiment du Doyen Jean Braconnier, 43 bd. du 11 novembre 1918, 69622 Villeurbanne Cedex, France; luca.zamboni@wanadoo.fr Reykjavik University, School of Computer Science, Kringlan 1, 103 Reykjavik, Iceland; lqz@ru.is
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Abstract

Among the various ways to construct a characteristic Sturmian word, one of the most used consists in defining an infinite sequence of prefixes that are standard. Nevertheless in any characteristic word c, some standard words occur that are not prefixes of c. We characterize all standard words occurring in any characteristic word (and so in any Sturmian word) using firstly morphisms, then standard prefixes and finally palindromes.

Keywords

Sturmian wordsstandard factorsmorphismspalindromes
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 44 , Issue 1: Special issue dedicated to the 12th "Journées Montoises d'Informatique Théorique" , January 2010 , pp. 159 - 174
Copyright
© EDP Sciences, 2010

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