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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)
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)
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)
For irrational β > 1 we consider the set Fin(β) of real numbers for which |x| has a finite number of non-zero digits in its expansion in base β. In particular, we consider the set of β-integers, i.e. numbers whose β-expansion is of the form n i=0 x i β i , n ≥ 0. We discuss some necessary and some sufficient conditions for Fin(β) to be a ring. We also(More)
We study infinite words coding an orbit under an exchange of three intervals which have full complexity C(n) = 2n + 1 for all n ∈ N (non-degenerate 3iet words). In terms of parameters of the interval exchange and the starting point of the orbit we characterize those 3iet words which are invariant under a primitive substitution. Thus, we generalize the(More)