3 problems

Let $\Sigma_k$ be a $k$-letter alphabet, and let $L_{k,\alpha}$ denote the language of $\alpha$-power-free finite words over $\Sigma_k$. For a language $L$, write ${\sf ext}(L)$ fo…

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…