A note on Tutte polynomials and Orlik–Solomon algebras

Let be a (central) arrangement of hyperplanes in and the dependence matroid of the linear forms . The Orlik–Solomon algebra of a matroid is the exterior algebra on the points modulo the ideal generated by circuit boundaries. The graded algebra is isomorphic to the cohomology algebra of the manifold . The Tutte polynomial is a powerful invariant of the matroid . When is a rank 3 matroid and the θ_Hi are complexifications of real linear forms, we will prove that determines . This result partially solves a conjecture of Falk.