2 problems

Fix $k\geqslant 1$. A word is called $k$-anagram-free if every factor $F$ satisfies $\alpha(F)\geqslant k+1$, where $\alpha(F)$ is the least number of cuts needed to decompose $F$…

Let $\mathbb{A}$ be an alphabet of size $r\geqslant 5$, and let $F$ be a factor of an extremal word over $\mathbb{A}$. The distance between consecutive occurrences of $F$ is measur…