7 problems

Let $\mathpzc{A}=\{a,b\}$ be an even or mixed binary alphabet, let $\mathcal{C}_f^\infty$ be the set of f-smooth words over $\mathpzc{A}$, and for a finite word $u$ let the frequen…

Sing's power-law conjecture. Over $\mathpzc{A}=\{a,b\}$,

Let $\mathpzc{A}=\{a,b\}$ be a mixed binary alphabet, let $\mathcal{C}^\infty$ be the set of infinite smooth words over $\mathpzc{A}$, let $\mathcal{C}_f^\infty$ be the set of fini…

Let $\mathpzc{A}=\{a,b\}$ be a binary alphabet, let $\mathcal{C}^\infty$ be the set of infinite smooth words over $\mathpzc{A}$, let $\mathcal{C}_f^\infty$ be the set of finite f-s…

Let $\mathpzc{A}=\{a,b\}$ be a binary alphabet, let $\mathcal{C}_f^\infty$ be the set of finite f-smooth words over $\mathpzc{A}$, and let $p_{\mathcal{C}_f^\infty}(n)$ denote its…

Let $\mathcal{C}_f^\infty$ be the set of finite f-smooth words over the binary alphabet $\{1,2\}$, and let $p_{\mathcal{C}_f^\infty}(n)$ denote the number of factors of length $n$…

A smooth factor is a finite factor of a smooth word, and an infinite smooth word is an infinite word satisfying the paper's smoothness condition over the alphabet $\{1,2\}$. Univer…