6 problems

Let $\varphi$ be a Pisot substitution on $n$ letters. Let $\tilde\varphi$ be a rewriting of $\varphi$ such that, for some letters $b,e$ in the rewritten alphabet,…

Let $(X,T)$ be a Toeplitz flow with period structure $(p_k)$, and let $c$ be a positive integer. A minimal speedup with orbit number $c$ means a minimal bounded speedup $(X,S)$ of…

Let $\theta$ be a constant-length left proper substitution and let $c>1$ satisfy $\gcd(c,|\theta|)=1$. If $l$ is a factor of $c$ with $1\leq l<c$, then $(X_\theta,T^l)$ and…

Let $\sigma$ be a Pisot irreducible substitution, meaning that the characteristic polynomial of its incidence matrix is the minimal polynomial of a Pisot number. Let…

Let $C_a(X)$ denote the characteristic function associated with the first letter $a$ of the Fibonacci substitution. The quantities $_n$ measure the left endpoints of intervals on w…

Independent-substitution conjecture. Then $x$ is ultimately periodic.