Geodesic
A Formula for Birational Rowmotion on Rectangles
Séminaire lotharingien de combinatoire, 80B (2018) 
Gregg Musiker; Tom Roby. A Formula for Birational Rowmotion on Rectangles. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a36/
@article{SLC_2018_80B_a36,
     author = {Gregg Musiker and Tom Roby},
     title = {A {Formula} for {Birational} {Rowmotion} on {Rectangles}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2018},
     volume = {80B},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a36/}
}
TY  - JOUR
AU  - Gregg Musiker
AU  - Tom Roby
TI  - A Formula for Birational Rowmotion on Rectangles
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a36/
ID  - SLC_2018_80B_a36
ER  - 
%0 Journal Article
%A Gregg Musiker
%A Tom Roby
%T A Formula for Birational Rowmotion on Rectangles
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a36/
%F SLC_2018_80B_a36

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

We give a formula in terms of families of non-intersecting lattice paths for iterated actions of the birational rowmotion map on a product of two chains, equivalently a rectangle. This allows us to give a much simpler direct proof of the key fact that the period of this map on a product of chains of lengths r and s is r+s+2 (first proved by D. Grinberg and the second author) as well as other consequences, as explained in [8].