Abstract:
For $\mathscr{B}\subset \mathbb{N}$, the corresponding $\mathscr{B}$-free subshift $X_\eta$ is the orbit closure of the characteristic function $\eta$ of $\mathscr{B}$-free integers $\mathbb{Z}\seminus \bigcup_{b\in\mathscr{B}}b\mathbb{Z}$. I will explain how to get a description of all invariant measures on $X_\eta$, under the assumption that its unique minimal subshift $X_{\eta^*}$ is a regular Toeplitz shift. This settles a conjecture formulated earlier by G. Keller.
(Joint work with Aurelia Dymek and Daniel Sell)