Geodesic
Toric Arrangements Associated to Graphs
Séminaire lotharingien de combinatoire, 78B (2017)

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We study certain toric arrangements associated to graphs. The arrangement depends on the choice of an integral lattice: we focus on the case of the (co)root lattice of type A, but also comment on the (simpler) case of the (co)weight lattice of type A. We obtain a combinatorial description for the intersection poset and derive several results on the characteristic polynomial and the arithmetic Tutte polynomial of the toric arrangement. The former counts proper colorings that satisfy an additional divisibility condition. By employing the Voronoi cell of the lattice, we show that the chambers of certain toric arrangements may be seen as equivalence classes for a canonical equivalence relation on the set of chambers of the corresponding linear arrangement. We study this relation in the graphic case. 

@article{SLC_2017_78B_a83,
     author = {Marcelo Aguiar and Swee Hong Chan},
     title = {Toric {Arrangements} {Associated} to {Graphs}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a83/}
}
TY  - JOUR
AU  - Marcelo Aguiar
AU  - Swee Hong Chan
TI  - Toric Arrangements Associated to Graphs
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a83/
ID  - SLC_2017_78B_a83
ER  - 
%0 Journal Article
%A Marcelo Aguiar
%A Swee Hong Chan
%T Toric Arrangements Associated to Graphs
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a83/
%F SLC_2017_78B_a83
Marcelo Aguiar; Swee Hong Chan. Toric Arrangements Associated to Graphs. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a83/