9 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…

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 $({\bf ftm}[n])_{n\geq 0}$ be the Fibonacci-Thue-Morse sequence, obtained by summing modulo $2$ the bits in the Fibonacci representation of $n$. Let $\rho_{\bf ftm}(n)$ denote…

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…

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