5 problems

Hollander's conjecture. If $L$ is regular, there exists $p$ such that the limit

Let $k$ be the length of the vector $\vec{\mathbf{c}}=(c_1,\ldots,c_k)$, and let the algorithm in the proof of Theorem main be the conversion algorithm for $\vec{\mathbf{c}}$-repre…

Let $\beta(N)=\beta^+(N)\cdot\beta^-(N)$ be the base-phi expansion of the number $N$. Let $w$ be a word of length $m$, and let $R_{\cdot w}$ be the sequence of occurrences of numbe…

Let $\zeta\in\mathbb{Z}_2$ be the $2$-adic number defined in Equation, and let $\ell_\zeta(a)$ denote the length of the zero block beginning at the relevant digit position indexed…

Let $G$ and $H$ be expansions whose corresponding recurrence relations have multiplicatively independent dominant roots. Let $H_G(n)$ and $H_H(n)$ denote the relevant expansion com…