11 problems

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…

Uniqueness conjecture. If there exists an $n$ such that $\Delta^2 f(n)=-1$, then there exists at most one infinite gap increasing word with subword complexity function $f$.

Let $x^{(00)}$ be the fixed point of the Thue–Morse two-block substitution, and let $p^{(00)}(n)$ denote its subword complexity, namely the number of distinct factors of length $n$…

Let ${\mathbf G}$ be the ternary infinite word defined earlier in the paper, and let the subword complexity of an infinite word be the number of its distinct factors of each length…

Let ${\mathbf T}$ be the ternary Thue word, the fixed point of the morphism $0\mapsto012$, $1\mapsto02$, and $2\mapsto1$. A ternary infinite word is square-free if it contains no f…

Let $a_k(n)$ denote the number of distinct subword complexity sequences of length $n \ge 1$ over a $k$-letter alphabet. Recurrence conjecture. There exists a function $f(k)$ such t…

Let $a_k(n)$ denote the number of distinct subword complexity sequences of length $n \ge 1$ over a $k$-letter alphabet. Asymptotic conjecture. … The conjecture is motivated by nume…

Let $a_k(n)$ denote the number of distinct subword complexity sequences of length $n \ge 1$ over a $k$-letter alphabet. Enayati and Green's conjecture. … This conjecture predicts t…

Dekking's conjecture. There is a suitable positive constant $c$ such that

Let $K$ be the Kolakoski sequence over the alphabet $\{1,2\}$. For each positive integer $n$, let $P_K(n)$ denote the number of subwords (factors) of length $n$ occurring in $K$, a…

Maximal complexity conjecture. The complexity of $\alpha$ satisfies