9 problems

Let ${\mathbf G}=\gamma^\omega(0)$, where $\gamma=[01,2,02]$, let $h$ be a morphism in Table, and let $h^R$ denote the reversed morphism used in that table. Let $\mu$ be the critic…

Let ${\mathbf G}=\gamma^\omega(0)$, where $\gamma=[01,2,02]$, and let $\mu$ be its critical exponent. For each morphism $h$ in Table, consider the infinite word $h({\mathbf G})$. M…

For each integer $k\geq 1$, let ${\bf x}_k$ be the infinite word defined as the limit of the locally catenative sequence described above, and let $\rho_{{\bf x}_k}(n)$ denote its s…

For each integer $k\geq 1$, let ${\bf x}_k$ be the infinite word defined as the limit of the locally catenative sequence described above. The critical exponent conjecture for…

Let $x^{(00)}$ be the Thue–Morse two-block fixed point, and let the frequency of $1$ mean the limiting proportion of positions occupied by $1$ in its prefixes, if that limit exists…

Let $x^{(00)}$ be the fixed point of the Thue–Morse two-block substitution. A word is uniformly recurrent when every finite factor occurring in $x^{(00)}$ occurs there with bounded…

Let $x^{(00)}$ be the fixed point of the Thue–Morse two-block substitution, and let $L_{\rm\sc TM}$ be the language of all finite words occurring in $x^{(00)}$. A set of binary wor…

Linear-length anti-power conjecture. There is a constant $C=C(W)$ such that, for all positive integers $i$ and $k$, $W$ contains a $k$-anti-power with blocks of length at most $Ck$…

Classification conjecture. Let $\mathbf u$ be an aperiodic binary generalized pseudostandard word, not standard Sturmian, being a fixed point of a primitive morphism. Then