2 problems

Rauzy-class decomposition conjecture. The extended Rauzy class $cmathfrak{R}_{ex}$ is a disjoint union of exactly $k$ nonempty Rauzy classes.

Boissy–Lanneau's equivalence conjecture. The sets $cmathfrak{R}_{ex}(cpi)$ and $cmathfrak{R}'_{ex}(cpi)$ coincide.