论文标题
飞机隔板的动力学：Cameron-fon-der-Flaass猜想的证明
Dynamics of plane partitions: Proof of the Cameron-Fon-Der-Flaass conjecture
论文作者
论文摘要
动态代数组合学中最古老的杰出问题之一是P. Cameron和D. Fon-der-Flaass（1995）的以下猜想。考虑一个$ a \ times b \ times c $ box $ {\ sf b} $中的平面分区$ p $。令$ψ（p）$表示包含$ {\ sf b} -p $的最小元素的最小平面分区。然后，如果$ p = a+b+c-1 $是Prime，则Cameron和Fon-der-Flaass猜想$ψ$ -Orbit的基数$ P $始终是$ p $的倍数。 这一猜想是由Cameron和Fon-der-Flaass（1995）以$ p \ gg 0 $建立的，而K. Dilks，J。Striker和第二作者（2017）的作品的值稍小。我们的主要定理专门证明这一猜想是完全普遍的。
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 $Ψ(P)$ 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 $Ψ$-orbit of $P$ is always a multiple of $p$. This conjecture was established for $p \gg 0$ by Cameron and Fon-Der-Flaass (1995) and for slightly smaller values of $p$ in work of K. Dilks, J. Striker, and the second author (2017). Our main theorem specializes to prove this conjecture in full generality.
