A note on Tutte polynomials and Orlik-Solomon algebras
Combinatorics
2012-01-19 v4 Algebraic Topology
Abstract
Let A be a (central) arrangement of hyperplanes in a finite dimension complex vector space V. Let M(A) be the dependence matroid determined by A. The Orlik-Solomon algebra OS(M) of a matroid M is the exterior algebra on the points modulo the ideal generated by circuit boundaries. The algebra OS(M) is isomorphic to the cohomology algebra of the complement in V of the union of the hyperplanes of A. The Tutte polynomial T(x,y) of M is a powerful invariant of the matroid M. When M(A) is a rank three matroid and A is the complexification of a real arrangement, we prove that OS(M) determines T(x,y). This result solves partially a conjecure of M. Falk.
Cite
@article{arxiv.math/0203152,
title = {A note on Tutte polynomials and Orlik-Solomon algebras},
author = {Raul Cordovil and David Forge},
journal= {arXiv preprint arXiv:math/0203152},
year = {2012}
}
Comments
6 pages, 3 figures to appear in European Journal of Combinatorics