2 problems

Let $k\ge3$, and let $U_k(n)$ denote the minimum number of cyclic runs in an aperiodic necklace of length $n$ whose Burrows–Wheeler image is completely unclustered, over an ordered…

Necklace invertibility conjecture. There exist infinitely many $n$, different from a power of $p$, for which every aperiodic necklace of length $n$ over $\Sigma_p$ with non-zero we…