Journal article
Quasiperiodic and Lyndon episturmian words
Theoretical Computer Science, Vol.409(3), pp.578-600
2008
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.
Details
- Title
- Quasiperiodic and Lyndon episturmian words
- Authors/Creators
- A. Glen (Author/Creator)F. Levé (Author/Creator)G. Richomme (Author/Creator)
- Publication Details
- Theoretical Computer Science, Vol.409(3), pp.578-600
- Publisher
- Elsevier BV
- Identifiers
- 991005542086407891
- Copyright
- © 2008 Elsevier B.V.
- Murdoch Affiliation
- Murdoch University
- Language
- English
- Resource Type
- Journal article
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- Citation topics
- 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