10 citations · 26 across the 18 of their papers we have counts for
24 papers
Generalized reflection complexity
Adam Blažek, Lubomíra Dvořáková, Edita Pelantová
The reflection complexity of a sequence, introduced recently by Allouche, Campbell, Li, Shallit, and Stipulanti, counts the factors of a given length up to reversal. We generalize…
Reflection on the reflection complexity
Lubomíra Dvořáková, Edita Pelantová
The factor complexity of a sequence over a finite alphabet counts the number of factors of length occurring in $\mat…
Attractors of sequences coding -integers
Lubomíra Dvořáková, Martina Moravcová
In this paper, we describe minimal string attractors of prefixes of simple Parry sequences. These sequences form a coding of distances between consecutive -integers in numeratio…
On a sequence of Kimberling and its relationship to the Tribonacci word
Lubomíra Dvořáková, Edita Pelantová, Jeffrey Shallit
In 2017, Clark Kimberling defined an interesting sequence of 's and 's by certain inflation rules, and he made a number of conjectures about thi…
The limit of repetition thresholds of rich sequences
Lubomíra Dvořáková, Edita Pelantová
The repetition threshold of a class of sequences is the smallest number such that a sequence from the class contains no repetition with exponent . We focus on the class $\…
Frequencies of letters in infinite -balanced sequences
Lubomíra Dvořáková, Edita Pelantová
Frequency of letters in a symbolic sequence over a finite alphabet is one of the basic characteristics of . The notion of -balancedness captures the property…
Critical exponent of ternary words with few distinct palindromes
Ľubomíra Dvořáková, Lucas Mol, Pascal Ochem
We study infinite ternary words that contain few distinct palindromes. In particular, we classify such words according to their critical exponent.
On two conjectures of Shallit about Thue-Morse-like sequences
Lubomíra Dvořáková, Savinien Kreczman, Edita Pelantová
We study a class of infinite words , where is a positive integer, recently introduced by J. Shallit. This class includes the Thue-Morse sequence , the Fibonacci-Thue…
The asymptotic repetition threshold of sequences rich in palindromes
Lubomíra Dvořáková, Karel Klouda, Edita Pelantová
The asymptotic critical exponent measures for a sequence the maximum repetition rate of factors of growing length. The infimum of asymptotic critical exponents of sequences of a ce…
2-balanced sequences coding rectangle exchange transformation
Lubomíra Dvořáková, Zuzana Masáková, Edita Pelantová
We define a new class of ternary sequences that are 2-balanced. These sequences are obtained by colouring of Sturmian sequences. We show that the class contains sequences of any gi…
Critical exponent of binary words with few distinct palindromes
L'ubomíra Dvořáková, Pascal Ochem, Daniela Opočenská
We study infinite binary words that contain few distinct palindromes. In particular, we classify such words according to their critical exponents. This extends results by Fici and…
The repetition threshold of episturmian sequences
Lubomíra Dvořáková, Edita Pelantová
The repetition threshold of a class of infinite -ary sequences is the smallest real number such that in the class there exists a sequence that avoids -powers for…
String attractors of Rote sequences
Lubomíra Dvořáková, Veronika Hendrychová
In this paper, we describe minimal string attractors (of size two) of pseudopalindromic prefixes of standard complementary-symmetric Rote sequences. Such a class of Rote sequences…
String attractors of episturmian sequences
Lubomíra Dvořáková
In this paper, we describe string attractors of all factors of episturmian sequences and show that their size is equal to the number of distinct letters contained in the factor.
Complement Avoidance in Binary Words
James Currie, L'ubomíra Dvořaková, Pascal Ochem +3
The complement of a binary word is obtained by changing each in to and vice versa. We study infinite binary words that avoid sufficiently lar…
Asymptotic repetitive threshold of balanced sequences
Lubomíra Dvořáková, Daniela Opočenská, Edita Pelantová
The critical exponent of an infinite sequence over a finite alphabet expresses the maximal repetition of a factor in . By the famous Dejean's…
On minimal critical exponent of balanced sequences
Lubomíra Dvořáková, Daniela Opočenská, Edita Pelantová +1
We study the threshold between avoidable and unavoidable repetitions in infinite balanced sequences over finite alphabets. The conjecture stated by Rampersad, Shallit and Vandomme…
On balanced sequences and their critical exponent
Francesco Dolce, Lubomira Dvorakova, Edita Pelantova
We study aperiodic balanced sequences over finite alphabets. A sequence vv of this type is fully characterised by a Sturmian sequence u and two constant gap sequences y and y'. We…
Antipalindromic numbers
Lubomira Dvorakova, Stanislav Kruml, David Ryzak
Everybody has certainly heard about palindromes: words that stay the same when read backwards. For instance kayak, radar, or rotor. Mathematicians are interested in palindromic num…
Complementary symmetric Rote sequences: the critical exponent and the recurrence function
Lubomíra Dvořáková, Kateřina Medková, Edita Pelantová
We determine the critical exponent and the recurrence function of complementary symmetric Rote sequences. The formulae are expressed in terms of the continued fraction expansions a…
Normalization of ternary generalized pseudostandard words
Josef Florian, Tereza Vesela, Lubomira Dvorakova
This paper focuses on generalized pseudostandard words, defined by de Luca and De Luca in 2006. In every step of the construction, the involutory antimorphism to be applied for the…
Fixed points of morphisms among binary generalized pseudostandard words
Lubomira Dvorakova, Tereza Velka
We introduce a class of fixed points of primitive morphisms among aperiodic binary generalized pseudostandard words. We conjecture that this class contains all fixed points of prim…
A new estimate on complexity of binary generalized pseudostandard words
Lubomira Dvorakova, Josef Florian
Generalized pseudostandard words were introduced by de Luca and De Luca in 2006. In comparison to the palindromic and pseudopalindromic closure, only little is known about the gene…
On periodicity of generalized pseudostandard words
Josef Florian, Lubomira Dvorakova
Generalized pseudostandard words were introduced by de Luca and De Luca in 2006. In comparison to the palindromic and pseudopalindromic closure, only little is known about the gene…