Séminaire Lotharingien de Combinatoire, 78B.84 (2017), 12 pp.
Marcelo Aguiar and Swee Hong Chan
Toric Arrangements Associated to Graphs
Abstract.
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.
Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.
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