9 citations · 23 across the 19 of their papers we have counts for
29 papers
Minimal and proximal examples of -stable and -approachable shift spaces
Melih Emin Can, Jakub Konieczny, Michal Kupsa +1
We study shift spaces over a finite alphabet that can be approximated by mixing shifts of finite type in the sense of (pseudo)metrics connected to Ornstein's metric ($\ba…
On asymptotically automatic sequences
Jakub Konieczny
We study the notion of an asymptotically automatic sequence, which generalises the notion of an automatic sequence. While -automatic sequences are characterised by finiteness of…
Bracket words along Hardy field sequences
Jakub Konieczny, Clemens Müllner
We study bracket words, which are a far-reaching generalisation of Sturmian words, along Hardy field sequences, which are a far-reaching generalisation of Piatetski--Shapiro sequen…
Pisot numbers, Salem numbers, and generalised polynomials
Jakub Byszewski, Jakub Konieczny
We study sets of integers that can be defined by the vanishing of a generalised polynomial expression. We show that this includes sets of values of linear recurrent sequences of Sa…
An asymptotic version of Cobham's theorem
Jakub Konieczny
We introduce the notion of an asymptotically automatic sequence, which generalises the notion of an automatic sequence, and we prove a variant of Cobham's theorem for the newly int…
Bracket words: a generalisation of Sturmian words arising from generalised polynomials
Boris Adamczewski, Jakub Konieczny
Generalised polynomials are maps constructed by applying the floor function, addition, and multiplication to polynomials. Despite superficial similarity, generalised polynomials ex…
On -approachability, entropy density and -free shifts
Jakub Konieczny, Michal Kupsa, Dominik Kwietniak
We study approximation schemes for shift spaces over a finite alphabet using (pseudo)metrics connected to Ornstein's metric. This leads to a class of shift spaces we call…
Characterisation of Meyer sets via the Freiman--Ruzsa theorem
Jakub Konieczny
We show that the Freiman--Ruzsa theorem, characterising finite sets with bounded doubling, leads to an alternative proof of a characterisation of Meyer sets, that is, relatively de…
Multiplicative automatic sequences
Jakub Konieczny, Mariusz Lemańczyk, Clemens Müllner
We obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.
Gowers norms for automatic sequences
Jakub Byszewski, Jakub Konieczny, Clemens Müllner
We show that any automatic sequence can be separated into a structured part and a Gowers uniform part in a way that is considerably more efficient than guaranteed by the Arithmetic…
Substitutive systems and a finitary version of Cobham's theorem
Jakub Byszewski, Jakub Konieczny, Elżbieta Krawczyk
We study substitutive systems generated by nonprimitive substitutions and show that transitive subsystems of substitutive systems are substitutive. As an application we obtain a co…
On multiplicative automatic sequences
Jakub Konieczny
We show that any automatic multiplicative sequence either coincides with a Dirichlet character or is identically zero when restricted to integers not divisible by small primes. Thi…
Generalised polynomials and integer powers
Jakub Konieczny
We show that there does not exist a generalised polynomial which vanishes precisely on the set of powers of two. In fact, if is and integer and $g \colon \mathbb{N} \to…
Algorithmic classification of noncorrelated binary pattern sequences
Jakub Konieczny
We show that it is possible to algorithmically verify if a given pattern sequence is noncorrelated. As an application, we compute that there are exactly noncorrelated binary…
Möbius orthogonality for -semimultiplicative sequences
Jakub Konieczny
We show that all -semimultiplicative sequences are asymptotically orthogonal to the Möbius function, thus proving the Sarnak conjecture for this class of sequences. This general…
On uniformity of -multiplicative sequences
Aihua Fan, Jakub Konieczny
We show that any -multiplicative sequence which is \emph{oscillating} of order , i.e.\ does not correlate with linear phase functions (, is Gow…
Factors of generalised polynomials and automatic sequences
Jakub Byszewski, Jakub Konieczny
The aim of this short note is to generalise the result of Rampersad--Shallit saying that an automatic sequence and a Sturmian sequence cannot have arbitrarily long common factors.…
A density version of Cobham's theorem
Jakub Byszewski, Jakub Konieczny
Cobham's theorem asserts that if a sequence is automatic with respect to two multiplicatively independent bases, then it is ultimately periodic. We prove a stronger density version…
Automatic sequences as good weights for ergodic theorems
Tanja Eisner, Jakub Konieczny
We study correlation estimates of automatic sequences (that is, sequences computable by finite automata) with polynomial phases. As a consequence, we provide a new class of good we…
Automatic sequences and generalised polynomials
Jakub Byszewski, Jakub Konieczny
We conjecture that bounded generalised polynomial functions cannot be generated by finite automata, except for the trivial case when they are ultimately periodic. Using methods fro…
Sparse generalised polynomials
Jakub Byszewski, Jakub Konieczny
We investigate generalised polynomials (i.e. polynomial-like expressions involving the use of the floor function) which take the value on all integers except for a set of densi…
Gowers norms for the Thue-Morse and Rudin-Shapiro sequences
Jakub Konieczny
We estimate Gowers uniformity norms for some classical automatic sequences, such as the Thue-Morse and Rudin-Shapiro sequences. The methods can also be extended to other automatic…
Automatic sequences, generalised polynomials, and nilmanifolds
Jakub Byszewski, Jakub Konieczny
We conjecture that bounded generalised polynomial functions cannot be generated by finite automata, except for the trivial case when they are periodic away from a finite set. Using…
Arcwise connectedness of the set of ergodic measures of hereditary shifts
Jakub Konieczny, Michal Kupsa, Dominik Kwietniak
We show that the set of ergodic invariant measures of a shift space with a safe symbol (this includes all hereditary shifts) is arcwise connected when endowed with the -bar metr…