3 problems

Fraenkel's conjecture. There is a unique, up to $\mathfrak{S}_{N}$-action, primitive circular balanced word $\mathbf{F}_{N}$ with pairwise distinct amounts of letters for…

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

Rampersad et al.'s conjecture. The smallest possible critical exponent of an infinite balanced word over a $5$-letter alphabet is