20 citations · 133 across the 31 of their papers we have counts for
33 papers
Circularity and repetitiveness in non-injective DF0L systems
Herman Goulet-Ouellet, Karel Klouda, Štěpán Starosta
We study circularity in DF0L systems, a generalization of D0L systems. We focus on two different types of circularity, called weak and strong circularity. When the morphism is inje…
Periodicity of general multidimensional continued fractions using repetend matrix form
Hanka Řada, Štěpán Starosta, Vítězslav Kala
We consider expansions of vectors by a general class of multidimensional continued fraction algorithms. If the expansion is eventually periodic, then we describe the possible struc…
Infinite Words and Morphic Languages Formalized in Isabelle/HOL
Štěpán Starosta
We present a formalization of basics related to infinite words in the generic proof assistant Isabelle/HOL. Furthermore, we present a formalization of purely morphic and morphic la…
Binary codes that do not preserve primitivity
Štěpán Holub, Martin Raška, Štěpán Starosta
A code is not primitivity preserving if there is a primitive list whose concatenation is imprimitive. We formalize a full characterization of su…
On a faithful representation of Sturmian morphisms
Jana Lepšová, Edita Pelantová, Štěpán Starosta
The set of morphisms mapping any Sturmian sequence to a Sturmian sequence forms together with composition the so-called monoid of Sturm. For this monoid, we defne a faithful repres…
The number of primitive words of unbounded exponent in the language of an HD0L-system is finite
Karel Klouda, Štěpán Starosta
Let be an HD0L-system. We show that there are only finitely many primitive words with the property that , for all integers , is an element of the factorial language…
Producing symmetrical facts for lists induced by the list reversal mapping in Isabelle/HOL
Martin Raška, Štěpán Starosta
Many facts possess symmetrical counterparts that often require a separate formal proof, depending on the nature of the involved symmetry. We introduce a method in Isabelle/HOL whic…
A characterization of Sturmian sequences by indistinguishable asymptotic pairs
Sebastián Barbieri, Sébastien Labbé, Štěpán Starosta
We give a new characterization of biinfinite Sturmian sequences in terms of indistinguishable asymptotic pairs. Two asymptotic sequences on a full -shift are indistingu…
Binary intersection formalized
Štěpán Holub, Štěpán Starosta
We provide a reformulation and a formalization of the classical result by Juhani Karhumäki characterizing intersections of two languages of the form . We u…
On Sturmian substitutions closed under derivation
Edita Pelantová, Štěpán Starosta
Occurrences of a factor in an infinite uniformly recurrent sequence can be encoded by an infinite sequence over a finite alphabet. This sequence is usually denoted ${…
On substitutions closed under derivation: examples
Václav Košík, Štěpán Starosta
We study infinite words fixed by a morphism and their derived words. A derived word is a coding of return words to a factor. We exhibit two examples of sets of morphisms which are…
Bounds on the period of the continued fraction after a Möbius transformation
Hanka Řada, Štěpán Starosta
We study Möbius transformations (also known as linear fractional transformations) of quadratic numbers. We construct explicit upper and lower bounds on the period of the continued…
Fixed points of Sturmian morphisms and their derivated words
Karel Klouda, Kateřina Medková, Edita Pelantová +1
Any infinite uniformly recurrent word can be written as concatenation of a finite number of return words to a chosen prefix of . Ordering of the return words…
On Words with the Zero Palindromic Defect
Edita Pelantová, Štěpán Starosta
We study the set of finite words with zero palindromic defect, i.e., words rich in palindromes. This set is factorial, but not recurrent. We focus on description of pairs of rich w…
On the Zero Defect Conjecture
Sébastien Labbé, Edita Pelantová, Štěpán Starosta
Brlek et al. conjectured in 2008 that any fixed point of a primitive morphism with finite palindromic defect is either periodic or its palindromic defect is zero. Bucci and Vaslet…
Markov constant and quantum instabilities
Edita Pelantová, Štěpán Starosta, Miloslav Znojil
For a qualitative analysis of spectra of certain two-dimensional rectangular-well quantum systems several rigorous methods of number theory are shown productive and useful. These m…
Exchange of three intervals: itineraries, substitutions and palindromicity
Zuzana Masáková, Edita Pelantová, Štěpán Starosta
Given a symmetric exchange of three intervals, we provide a detailed description of the return times to a subinterval and the corresponding itineraries. We apply our results to mor…
Morphic images of episturmian words having finite palindromic defect
Štěpán Starosta
We study morphisms from certain classes and their action on episturmian words. The first class is . In general, a morphism of class can map an infinite word havi…
Constructions of words rich in palindromes and pseudopalindromes
Edita Pelantová, Štěpán Starosta
A narrow connection between infinite binary words rich in classical palindromes and infinite binary words rich simultaneously in palindromes and pseudopalindromes (the so-called $H…
Characterization of circular D0L systems
Karel Klouda, Štěpán Starosta
We prove that every non-circular D0L system contains arbitrarily long repetitions. This result was already published in 1993 by Mignosi and Séébold, however their proof is only a s…
An Algorithm Enumerating All Infinite Repetitions in a D0L System
Karel Klouda, Štěpán Starosta
We describe a simple algorithm which, for a given D0L system, returns all factors such that is in the language of the system for all . This algorithm can be used to de…
Palindromic closures using multiple antimorphisms
Tatiana Jajcayová, Edita Pelantová, Štěpán Starosta
Generalized pseudostandard word , as introduced in 2006 by de Luca and De Luca, is given by a directive sequence of letters from an alphabet and by a directive se…
On the partitions with Sturmian-like refinements
Michal Kupsa, Štepán Starosta
In the dynamics of a rotation of the unit circle by an irrational angle , we study the evolution of partitions whose atoms are finite unions of left-closed right-open in…
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…