2 problems

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The Rauzy-class decomposition conjecture for extended Rauzy classes
Rauzy-class decomposition conjecture. The extended Rauzy class $cmathfrak{R}_{ex}$ is a disjoint union of exactly $k$ nonempty Rauzy classes.
Conjectureopenabelian-differentials flat-surfaces rauzy-classesarXiv posted 2 days ago
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Boissy–Lanneau's equivalence conjecture for extended Rauzy classes
Boissy–Lanneau's equivalence conjecture. The sets $cmathfrak{R}_{ex}(cpi)$ and $cmathfrak{R}'_{ex}(cpi)$ coincide.
Conjectureopenflat-surfaces quadratic-differentials rauzy-classesarXiv posted 2 days ago

The Rauzy-class decomposition conjecture for extended Rauzy classes