Dynamics of plane partitions: Proof of the Cameron–Fon-Der-Flaass conjecture

Abstract

One of the oldest outstanding problems in dynamical algebraic combinatorics is the following conjecture of P. Cameron and D. Fon-Der-Flaass (1995): consider a plane partition P in an $a \times b \times c$ box ${\sf B}$ . Let $\Psi (P)$ denote the smallest plane partition containing the minimal elements of ${\sf B} - P$ . Then if $p= a+b+c-1$ is prime, Cameron and Fon-Der-Flaass conjectured that the cardinality of the $\Psi $ -orbit of P is always a multiple of p.

Keywords

• 05E18
• 05A17