3 problems

Equivariant-bijection conjecture. Assuming the $m=1$ case of the preceding conjecture, there exists a $\mathbb Z/2h\mathbb Z$-equivariant bijection

Panyushev's order-divisibility conjecture. The order of $C$ always divides $2h$.

Let $J([\ell]\times[m]\times[n])$ be the set of order ideals in the product of chains, and suppose that $m+n+\ell-1=p$ is prime. Cameron–Fon-der-Flaass conjecture. The restriction…