5 problems

Samsonov–Shur's conjecture. The exact values are

Limit conjecture. The repetition thresholds of rich words satisfy

Dvořáková–Opočenská–Pelantová–Shur conjecture. For every odd integer $k\geq 13$,

Petrova–Shur's conjecture. The Abelian repetition thresholds satisfy

Repetition threshold conjecture. The value $c$ is the repetition threshold for the binary alphabet; equivalently, $RT(2)=c$.