39 citations · 63 across the 7 of their papers we have counts for
8 papers
Arithmetical subword complexity of automatic sequences
Jakub Konieczny, Clemens Müllner
We fully classify automatic sequences over a finite alphabet with the property that each word over appears is along an arithmetic progression. Using the terminology…
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…
Automaticity of uniformly recurrent substitutive sequences
Elżbieta Krawczyk, Clemens Müllner
We provide a complete characterisation of automaticity of uniformly recurrent substitutive sequences in terms of the incidence matrix of the return substitution of the underlying p…
Primes as sums of Fibonacci numbers
Michael Drmota, Clemens Müllner, Lukas Spiegelhofer
The purpose of this paper is to discuss the relationship between prime numbers and sums of Fibonacci numbers. One of our main results says that for every sufficiently large integer…
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…
The Rudin-Shapiro sequence and similar sequences are normal along squares
Clemens Müllner
We prove that digital sequences modulo along squares are normal, which covers some prominent sequences like the sum of digits in base modulo , the Rudin-Shapiro sequence…
Automatic sequences fulfill the Sarnak conjecture
Clemens Müllner
We present in this paper a new method to deal with automatic sequences. This method allows us to prove a Möbius-randomness-principle for automatic sequences from which we deduce th…
Normality of the Thue--Morse sequence along Piatetski-Shapiro sequences, II
Clemens Müllner, Lukas Spiegelhofer
We prove that the Thue--Morse sequence along subsequences indexed by is normal, where . That is, for in this range and for each $ω\in\…