8 problems

Let $f$ be the infinite Fibonacci word, let $C_f$ be its closed-rich constant, and let $\phi=\frac{1+\sqrt{5}}{2}$ be the golden ratio. Fibonacci closed-rich constant conjecture. F…

Let $f$ be the infinite Fibonacci word, let $\Sigma$ be its alphabet, and define … Here $\operatorname{Cl}(w)$ is the number of distinct closed factors of $w$, and $F_n$ denotes th…

The asymptotic bound conjecture. For all $d\geq 1$,

The Fibonacci-index formula conjecture.

Fibonacci nonautomaticity conjecture. The sequence $d_f$ of the Fibonacci word $\mathbf{u}_f$ is not Fibonacci-automatic, and consequently the prefix palindromic length…

Let $F_n$ be an even Fibonacci number, where the Fibonacci numbers satisfy the usual recurrence, and let $\mathbf{f}$ denote the Fibonacci word. A $k$-antipower is a concatenation…

Fibonacci word palindromic-length conjecture.

Let $\boldsymbol{f}$ be the Fibonacci word, namely the fixed point of the morphism $0\mapsto 01$, $1\mapsto 0$. Let $\tau$ denote the golden ratio. Frid's Fibonacci-word lower-boun…