Geodesic
Dynamics of plane partitions: Proof of the Cameron–Fon-Der-Flaass conjecture
Forum of Mathematics, Sigma, Tome 8 (2020)

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
@article{10_1017_fms_2020_61,
     author = {Rebecca Patrias and Oliver Pechenik},
     title = {Dynamics of plane partitions: {Proof} of the {Cameron{\textendash}Fon-Der-Flaass} conjecture},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {8},
     year = {2020},
     doi = {10.1017/fms.2020.61},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2020.61/}
}
TY  - JOUR
AU  - Rebecca Patrias
AU  - Oliver Pechenik
TI  - Dynamics of plane partitions: Proof of the Cameron–Fon-Der-Flaass conjecture
JO  - Forum of Mathematics, Sigma
PY  - 2020
VL  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1017/fms.2020.61/
DO  - 10.1017/fms.2020.61
LA  - en
ID  - 10_1017_fms_2020_61
ER  - 
%0 Journal Article
%A Rebecca Patrias
%A Oliver Pechenik
%T Dynamics of plane partitions: Proof of the Cameron–Fon-Der-Flaass conjecture
%J Forum of Mathematics, Sigma
%D 2020
%V 8
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1017/fms.2020.61/
%R 10.1017/fms.2020.61
%G en
%F 10_1017_fms_2020_61
Rebecca Patrias; Oliver Pechenik. Dynamics of plane partitions: Proof of the Cameron–Fon-Der-Flaass conjecture. Forum of Mathematics, Sigma, Tome 8 (2020). doi: 10.1017/fms.2020.61

Cité par Sources :