On reconstructing arrangements from their sets of simplices

AbstractLet GH(S,H) be the bipartite graph with partition sets S and H, the set of simplices and hyperplanes of H, where simplex s∈S is adjacent to hyperplane h∈H if one facet of s lies on h. In this paper, we give a complete characterization of GH(S,H) when H is a Γ-arrangement. We also study GH(S,H) when H is a pseudoline arrangement