3 problems

Limit conjecture. The repetition thresholds of rich words satisfy

Let $\operatorname{A}$ be a finite alphabet. For a finite nonempty rich word $w$ over $\operatorname{A}$, write its UPS-factorization as $w=w_pw_{p-1}\cdots w_1$, where the factors…

Let $r(n)$ be the maximum length of a rich square-free word over an alphabet of size $n$, and let $w_n$ be the recursively constructed rich square-free word over an alphabet of siz…