Geodesic
A Tropical Isoperimetric Inequality
Séminaire lotharingien de combinatoire, 78B (2017)

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

We introduce tropical analogues of the notion of volume of polytopes, leading to a tropical version of the (discrete) classical isoperimetric inequality. The planar case is elementary, but a higher-dimensional generalization leads to an interesting class of ordinary convex polytopes, characterizing the equality case in the isoperimetric inequality. This study is motivated by open complexity questions concerning linear optimization and its tropical analogs. 

@article{SLC_2017_78B_a26,
     author = {Jules Depersin and St\'ephane Gaubert and Michael Joswig},
     title = {A {Tropical} {Isoperimetric} {Inequality}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a26/}
}
TY  - JOUR
AU  - Jules Depersin
AU  - Stéphane Gaubert
AU  - Michael Joswig
TI  - A Tropical Isoperimetric Inequality
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a26/
ID  - SLC_2017_78B_a26
ER  - 
%0 Journal Article
%A Jules Depersin
%A Stéphane Gaubert
%A Michael Joswig
%T A Tropical Isoperimetric Inequality
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a26/
%F SLC_2017_78B_a26
Jules Depersin; Stéphane Gaubert; Michael Joswig. A Tropical Isoperimetric Inequality. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a26/