16 citations · 71 across the 14 of their papers we have counts for
12 papers · 1 filter
On Periodicity and Complexity of Generalized Pseudostandard Words
Josef Florian, Lubomira Balkova
Generalized pseudostandard words have been introduced by de Luca and De Luca in 2006. In comparison to the palindromic and pseudopalindromic closure, only little is known about the…
Aperiodic pseudorandom number generators based on infinite words
Lubomira Balkova, Michelangelo Bucci, Alessandro De Luca +2
In this paper we study how certain families of aperiodic infinite words can be used to produce aperiodic pseudorandom number generators (PRNGs) with good statistical behavior. We i…
Proof of Brlek-Reutenauer conjecture
Lubomira Balkova, Edita Pelantova, Stepan Starosta
Brlek and Reutenauer conjectured that any infinite word u with language closed under reversal satisfies the equality 2D(u) = \sum_{n=0}^{\infty}T_u(n) in which D(u) denotes the def…
Factor frequencies in generalized Thue-Morse words
Lubomira Balkova
We describe factor frequencies of the generalized Thue-Morse word t_{b,m} defined for integers b greater than 1, m greater than 0 as the fixed point starting in 0 of the morphism ϕ…
Factor frequencies in languages invariant under more symmetries
Lubomira Balkova
The number of frequencies of factors of length in a recurrent aperiodic infinite word does not exceed $3Δ\C(n)$, where $Δ\C (n)$ is the first difference of factor complexity,…
Abelian Complexity of Infinite Words Associated with Quadratic Parry Numbers
Ľubomíra Balková, Karel Břinda, Ondřej Turek
We derive an explicit formula for the Abelian complexity of infinite words associated with quadratic Parry numbers.
Infinite Words with Finite Defect
Lubomíra Balková, Edita Pelantová, Štěpán Starosta
In this paper, we provide a new characterization of uniformly recurrent words with finite defect based on a relation between the palindromic and factor complexity. Furthermore, we…
Sturmian Jungle (or Garden?) on Multiliteral Alphabets
Lubomira Balkova, Edita Pelantova, Stepan Starosta
The properties characterizing Sturmian words are considered for words on multiliteral alphabets. We summarize various generalizations of Sturmian words to multiliteral alphabets an…
A Note on Symmetries in the Rauzy Graph and Factor Frequencies
L. Balkova, E. Pelantova
We focus on infinite words with languages closed under reversal. If frequencies of all factors are well defined, we show that the number of different frequencies of factors of leng…
Palindromes in infinite ternary words
Lubomira Balkova, Edita Pelantova, Stepan Starosta
We study infinite words u over an alphabet A satisfying the property P : P(n)+ P(n+1) = 1+ #A for any n in N, where P(n) denotes the number of palindromic factors of length n occur…
Repetitions in beta-integers
L. Balková, K. Klouda, E. Pelantová
Classical crystals are solid materials containing arbitrarily long periodic repetitions of a single motif. In this paper, we study the maximal possible repetition of the same motif…
Sequences with constant number of return words
Lubomira Balkova, Edita Pelantova, Wolfgang Steiner
An infinite word has the property if every factor has exactly return words. Vuillon showed that characterizes Sturmian words. We prove that a word satisfies i…