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Standard factors of Sturmian words

Published online by Cambridge University Press:  11 February 2010

Gwénaël Richomme
Université de Picardie Jules Verne, Laboratoire MIS (Modélisation, Information, Systèmes), 33 rue Saint Leu, 80039 Amiens Cedex 1, France; Université Paul-Valéry Montpellier 3, UFR 4, Dpt. MIAp, Route de Mende, 34199 Montpellier Cedex 5,
Kalle Saari
Department of Mathematics and Turku Centre for Computer Science, University of Turku, 20014 Turku, Finland;
Luca Q. Zamboni
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; Reykjavik University, School of Computer Science, Kringlan 1, 103 Reykjavik, Iceland;
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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.

Research Article
© EDP Sciences, 2010

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