Geodesic
A Simple Explicit Bijection Between (n,2)-Gog and Magog Trapezoids
Séminaire lotharingien de combinatoire, Tome 75 (2016-2019) 
Jérémie Bettinelli. A Simple Explicit Bijection Between (n,2)-Gog and Magog Trapezoids. Séminaire lotharingien de combinatoire, Tome 75 (2016-2019). http://geodesic.mathdoc.fr/item/SLC_2016-2019_75_a4/
@article{SLC_2016-2019_75_a4,
     author = {J\'er\'emie Bettinelli},
     title = {A {Simple} {Explicit} {Bijection} {Between} {(n,2)-Gog} and {Magog} {Trapezoids}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2016-2019},
     volume = {75},
     url = {http://geodesic.mathdoc.fr/item/SLC_2016-2019_75_a4/}
}
TY  - JOUR
AU  - Jérémie Bettinelli
TI  - A Simple Explicit Bijection Between (n,2)-Gog and Magog Trapezoids
JO  - Séminaire lotharingien de combinatoire
PY  - 2016-2019
VL  - 75
UR  - http://geodesic.mathdoc.fr/item/SLC_2016-2019_75_a4/
ID  - SLC_2016-2019_75_a4
ER  - 
%0 Journal Article
%A Jérémie Bettinelli
%T A Simple Explicit Bijection Between (n,2)-Gog and Magog Trapezoids
%J Séminaire lotharingien de combinatoire
%D 2016-2019
%V 75
%U http://geodesic.mathdoc.fr/item/SLC_2016-2019_75_a4/
%F SLC_2016-2019_75_a4

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

A sub-problem of the open problem of finding an explicit bijection between alternating sign matrices and totally symmetric self-complementary plane partitions consists in finding an explicit bijection between so-called (n,k)-Gog trapezoids and (n,k)-Magog trapezoids. A quite involved bijection was found by Biane and Cheballah in the case k=2. We give here a simpler bijection for this case.