16 citations · 36 across the 9 of their papers we have counts for
7 papers · 1 filter
Minimality of -free systems in number fields
Aurelia Dymek, Stanisław Kasjan, Joanna Kułaga-Przymus
Let be a finite extension of and be its ring of integers. Let be a primitive collection of ideals in . We show that a…
Automorphisms of -free and other Toeplitz shifts
Aurelia Dymek, Stanisław Kasjan, Gerhard Keller
We present sufficient conditions for the triviality of the automorphism group of regular Toeplitz subshifts and give a broad class of examples from the class of -free…
Dynamics of -free sets: a view through the window
Stanisław Kasjan, Gerhard Keller, Mariusz Lemańczyk
Let be an infinite subset of . We characterize arithmetic and dynamical properties of the -free set through group…
-free sets and dynamics
Aurelia Bartnicka, Stanisław Kasjan, Joanna Kułaga-Przymus +1
Let and let be the characteristic function of the set of B-free numbers. Consider $…
Odometers and Toeplitz systems revisited in the context of Sarnak's conjecture
Tomasz Downarowicz, Stanislaw Kasjan
Although Sarnak's conjecture holds for compact group rotations (irrational rotations, odometers), it is not even known whether it holds for all Jewett-Krieger models of such rotati…
Polynomial actions of unitary operators and idempotent ultrafilters
Vitaly Bergelson, Stanisław Kasjan, Mariusz Lemańczyk
Let be an idempotent ultrafilter over . For a positive integer , let denote the additive group of polynomials with ${\rm…
0-1 sequences of the Thue-Morse type and Sarnak's conjecture
El Houcein El Abdalaoui, Stanisław Kasjan, Mariusz Lemańczyk
We show that the images via of the continuous part of the spectral measures of the dynamical systems generated by the 0-1 sequences of the Thue-Morse type are pairwi…