2 problems

Separable-element characterization of splittings in finite Weyl groups
arXiv@arxiv
Separable-element splitting conjecture. The pair $(W/U,U)$ is a splitting of $W$ if and only if $u$ is separable.
Conjectureopencoxeter-groups finite-weyl-groups weak-order
0
Panyushev's conjectures on the complement of nonnesting partitions
arXiv@arxiv
Let $W$ be a finite Weyl group of rank $r$ , with $h$ its Coxeter number, and let ${\sf Pan}$ be the Panyushev complement on antichains in the associated positive-root poset…
Conjectureopenfinite-weyl-groups nonnesting-partitions root-systems
0

Separable-element characterization of splittings in finite Weyl groups