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Title: 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 . 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.  more » « less
Award ID(s):
1703696
PAR ID:
10216219
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Forum of Mathematics, Sigma
Volume:
8
ISSN:
2050-5094
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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