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We characterize all quasiperiodic Sturmian words: a Sturmian word is not quasiperiodic if and only if it is a Lyndon word. Moreover, we study links between Sturmian morphisms and quasiperiodicity.

We prove that episturmian words and Arnoux-Rauzy sequences can be characterized using a local balance property. We also give a new characterization of epistandard words. Important remark: The first version of this LaRIA Research Report 2007-02 contained an error in the proof of a result stating the non-context-freeness of the complement of the set of finite… (More)

G. Rauzy showed that the Tribonacci minimal subshift generated by the morphism τ : 0 → 01, 1 → 02 and 2 → 0 is measure-theoretically conjugate to an exchange of three fractal domains on a compact set in R 2 , each domain being translated by the same vector modulo a lattice. In this paper we study the Abelian complexity ρ(n) of the Tribonacci word t which is… (More)

The notion of Abelian complexity of infinite words was recently used by the three last authors to investigate various Abelian properties of words. In particular, using van der Waerden's theorem, they proved that if a word avoids Abelian k-powers for some integer k, then its Abelian complexity is unbounded. This suggests the following question: How… (More)

Words 2005-Conjugacy of morphisms and Lyndon decomposition of standard Sturmian words – p.1/11

The S-adic conjecture postulates the existence of a condition C such that a sequence has linear complexity if and only if it is an S-adic sequence satisfying C for some finite set S of morphisms. We present an overview of the factor complexity of S-adic sequences and we give some examples that either illustrate some interesting properties, or that are… (More)