Geodesic
Plabic Graphs and Zonotopal Tilings
Séminaire lotharingien de combinatoire, 80B (2018)

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We introduce the notion of chord separation of two sets which generalizes Leclerc and Zelevinsky's weak separation. We show that every maximal by inclusion collection of pairwise chord separated sets is also maximal by size. Moreover, we prove that such collections are in bijection with fine zonotopal tilings of the three-dimensional cyclic zonotope. As a result, we get that Postnikov's reduced plabic graphs are precisely the objects dual to horizontal sections of zonotopal tilings of the three-dimensional cyclic zonotope, and Postnikov's moves on plabic graphs correspond to flips of these zonotopal tilings. 

@article{SLC_2018_80B_a67,
     author = {Pavel Galashin},
     title = {Plabic {Graphs} and {Zonotopal} {Tilings}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a67/}
}
TY  - JOUR
AU  - Pavel Galashin
TI  - Plabic Graphs and Zonotopal Tilings
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a67/
ID  - SLC_2018_80B_a67
ER  - 
%0 Journal Article
%A Pavel Galashin
%T Plabic Graphs and Zonotopal Tilings
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a67/
%F SLC_2018_80B_a67
Pavel Galashin. Plabic Graphs and Zonotopal Tilings. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a67/