Given a set B of natural numbers, we say that an integer n is B-free, if no
number in B divides n. In 2010 Sarnak initiated the study of the dynamics of
sets of B-free numbers. The orbit closure of the characteristic function of B-free
numbers is endowed with the left shift and called B-free subshift. Any B-free
system contains a unique minimal subshift. Moreover, it is minimal precisely if
the characteristic function of B-free integers is a Toeplitz sequence. Equivalently,
there is no "rescalled copy of an infinite pairwise coprime subset" in B. I will
discuss these results and their multidimensional counterparts.
The talk is based on the joint work with Stanisław Kasjan and Joanna Kułaga-
Przymus.