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We study the relation between the palindromic and factor complexity of infinite words. We show that for uniformly recurrent words one has P(n) + P(n + 1) ≤ ∆C(n) + 2, for all n ∈ N. For a large class of words it is a better estimate of the palindromic complexity in terms of the factor complexity then the one presented in [2]. We provide several examples of(More)
Keywords: Defect Rich word Full word Infinite word Factor complexity Palindromic complexity a b s t r a c t Brlek and Reutenauer conjectured that any infinite word u with language closed under reversal satisfies the equality 2D(u) = ∑ +∞ n=0 T u (n) in which D(u) denotes the defect of u and T u (n) denotes C u (n + 1) − C u (n) + 2 − P u (n + 1) − P u (n),(More)
A simple Parry number is a real number β > 1 such that the Rényi expansion of 1 is finite, of the form d β (1) = t 1 · · · t m. We study the palindromic structure of infinite aperiodic words u β that are the fixed point of a substitution associated with a simple Parry number β. It is shown that the word u β contains infinitely many palindromes if and only(More)
An infinite word has the property Rm if every factor has exactly m return words. Vuillon showed that R 2 characterizes Sturmian words. We prove that a word satisfies Rm if its complexity function is (m − 1)n + 1 and if it contains no weak bispecial factor. These conditions are necessary for m = 3, whereas for m = 4 the complexity function need not be 3n +(More)
We provide a complete characterization of substitution invariant inhomogeneous bi-directional pointed Sturmian sequences. The result is analogous to that obtained by Berthé et al. [5] and Yasutomi [21] for one-directional Sturmian words. The proof is constructive , based on the geometric representation of Sturmian words by a cut-and-project scheme.
A Parry number is a real number β > 1 such that the Rényi β-expansion of 1 is finite or infinite eventually periodic. If this expansion is finite, β is said to be a simple Parry number. Remind that any Pisot number is a Parry number. In a previous work we have determined the complexity of the fixed point u β of the canonical substitution associated with(More)