Link complexes of subspace arrangements

Abstract. Given a simplicial hyperplane arrangement H and a subspace arrangement A embedded in H, we define a simplicial complex ∆A,H as the subdivision of the link of A induced by H. In particular, this generalizes Steingr´ımsson’s coloring complex of a graph. We do the following: (1) When A is a hyperplane arrangement, ∆A,H is shown to be shellable. As a special case, we answer affirmatively a question of Steingr´ımsson on coloring complexes. (2) For H being a Coxeter arrangement of type A or B we obtain a close connection between the Hilbert series of the Stanley-Reisner ring of ∆A,H and the characteristic polynomial of A. This extends results of Steingr´ımsson and provides an interpretation of chromatic polynomials of hypergraphs and signed graphs in terms of Hilbert polynomials.

• Type: Journal
• Year: 2007
• Where: EJC
• Authors: Axel Hultman
• Keywords: EJC 2007, Hyperplane Arrangement, Information Technology, Simplicial Hyperplane Arrangement, Subspace Arrangement