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Journals and Conferences
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 . We provide several examples of… (More)
We study the properties of the function R (m) (n) defined as the number of representations of an integer n as a sum of distinct m-Bonacci numbers F
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.  and Yasutomi  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 add a sufficient condition for validity of Proposition 4.10 in the paper Frougny et al. (2004). This condition is not a necessary one, it is nevertheless convenient, since anyway most of the statements in the paper Frougny et al. (2004) use it.
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)