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Quasiperiodic and Lyndon episturmian words
Journal article   Open access   Peer reviewed

Quasiperiodic and Lyndon episturmian words

A. Glen, F. Levé and G. Richomme
Theoretical Computer Science, Vol.409(3), pp.578-600
2008
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Abstract

Recently the second two authors characterized quasiperiodic Sturmian words, proving that a Sturmian word is non-quasiperiodic if and only if, it is an infinite Lyndon word. Here we extend this study to episturmian words (a natural generalization of Sturmian words) by describing all the quasiperiods of an episturmian word, which yields a characterization of quasiperiodic episturmian words in terms of their directive words. Even further, we establish a complete characterization of all episturmian words that are Lyndon words. Our main results show that, unlike the Sturmian case, there is a much wider class of episturmian words that are non-quasiperiodic, besides those that are infinite Lyndon words. Our key tools are morphisms and directive words, in particular normalized directive words, which we introduced in an earlier paper. Also of importance is the use of return words to characterize quasiperiodic episturmian words, since such a method could be useful in other contexts.

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9 Mathematics
9.28 Pure Maths
9.28.534 Dynamical Systems
Web Of Science research areas
Computer Science, Theory & Methods
ESI research areas
Computer Science
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