Cameron–Fon-Der-Flaass periodicity conjecture for plane partitions

Fix positive integers $a,b,c$ and let $\mathsf{B}_{a,b,c}={\bf a}\times{\bf b}\times{\bf c}$ be the product of three chains. Let $J(\mathsf{B}_{a,b,c})$ denote its order ideals, and define rowmotion $\Psi$ by sending an order ideal to the order ideal generated by the minimal elements of its complementary order filter. For a $\Psi$-orbit, consider its cardinality. Cameron–Fon-Der-Flaass conjecture. If $p=a+b+c-1$ is prime, then the cardinality of every $\Psi$-orbit of $J(\mathsf{B}_{a,b,c})$ is a multiple of $p$. The conjecture asserts a uniform periodicity property for rowmotion on plane partitions. The paper proves this conjecture, so the claim is solved.