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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)

- Miloslav Havĺıček, Jǐŕı Patera, Edita Pelantová
- 2000

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)

- Peter Balázi, Zuzana Masáková, Edita Pelantová
- Theor. Comput. Sci.
- 2007

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)

- Lubomíra Balková, Edita Pelantová, Wolfgang Steiner
- ArXiv
- 2006

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)

Article history: Received 27 September 2010 Accepted 9 November 2010 Available online 12 January 2011

- Edita Pelantová, Steiner
- 2006

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)

- Zuzana Masáková, Edita Pelantová, Tomás Vávra
- Theor. Comput. Sci.
- 2011

- Edita Pelantová, Stepán Starosta
- Discrete Mathematics
- 2013

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)

- Edita Pelantová, Stepán Starosta
- Theor. Comput. Sci.
- 2014

- Christiane Frougny, Edita Pelantová, Milena Svobodová
- Theor. Comput. Sci.
- 2011

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)