Edita Pelantová

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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)
Maximal Abelian subgroups of Diagonalizable automorphisms of Lie algebra (so called MAD-groups) play the crucial role for construction of fine gradings of Lie algebra. Our aim is to give a description of MAD-groups for real forms of classical Lie algebras. We introduce four types of subgroups of matrices in Gl(n,C) called Out-groups, Ad-groups, Out∗-groups(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)
An infinite word has the property Rm if every factor has exactly m return words. Vuillon showed that R2 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 + 1. New(More)
We present three simple ideas which enable to determine easily the number of return words in some infinite words. Using these ideas, we give a new and very short proof of the fact that each factor of an Arnoux-Rauzy word of order m has exactly m return words. We describe the structure of return words for the Thue-Morse sequence and focus on infinite words(More)
Factor complexity C and palindromic complexity P of infinite words with language closed under reversal are known to be related by the inequality P(n) + P(n + 1) ≤ 2 + C(n + 1) − C(n) for any n ∈ N . Word for which the equality is attained for any n is usually called rich in palindromes. In this article we study words whose languages are invariant under a(More)
We consider numeration systems where digits are integers and the base is an algebraic number β such that |β| > 1 and β satisfies a polynomial where one coefficient is dominant in a certain sense. For this class of bases β, we can find an alphabet of signed-digits on which addition is realizable by a parallel algorithm in constant time. This algorithm is a(More)