Zuzana Masáková

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The aim of this article is to study certain combinatorial properties of infinite binary and ternary words associated to cut-and-project sequences. We consider here the cut-and-project scheme in two dimensions with general orientation of the projecting subspaces. We prove that a cut-and-project sequence arising in such a setting has always either two or(More)
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 dβ(1) = t1 · · · tm. We study the palindromic structure of infinite aperiodic words uβ that are the fixed point of a substitution associated with a simple Parry number β. It is shown that the word uβ contains infinitely many palindromes if and only if t1 =(More)
We provide a complete characterization of substitution invariant inhomogeneous bidirectional 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.
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. Mathematics Subject Classification. 11A63, 11A67, 37B10, 68R15 RAIRO-Inf. Theor. Appl. 38 (2004) 163-185.
We study non-standard number systems with negative base −β. Instead of the ItoSadahiro definition, based on the transformation T−β of the interval [ − β β+1 , 1 β+1 ) into itself, we suggest a generalization using an interval [l, l + 1) with l ∈ (−1, 0]. Such generalization may eliminate certain disadvantages of the Ito-Sadahiro system. We focus on the(More)
We study matrices of morphisms preserving the family of words coding 3-interval exchange transformations. It is well known that matrices of morphisms preserving sturmian words (i.e. words coding 2-interval exchange transformations with the maximal possible factor complexity) form the monoid {M ∈ N | det M = ±1} = {M ∈ N | MEM = ±E}, where E = ( 0 1 −1 0 ).(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)