2 problems

Let $\kappa_{2,1}$ denote the Oldenburger–Kolakoski word over $\{1,2\}$, and interpret the frequency of a letter as its limiting proportion among prefixes, when that limit exists.…

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…