  Given a simplicial hyperplane arrangement H and a subspace arrangement A
embedded in H, we define a simplicial complex Delta_{A,H} as the subdivision of
the link of A induced by H. In particular, this generalizes Steingrimsson's
coloring complex of a graph.
  We do the following:
  (1) When A is a hyperplane arrangement, Delta_{A,H} is shown to be shellable.
As a special case, we answer affirmatively a question of Steingrimsson 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
Delta_{A,H} and the characteristic polynomial of A. This extends results of
Steingrimsson and provides an interpretation of chromatic polynomials of
hypergraphs and signed graphs in terms of Hilbert polynomials.

Combinatorics;Commutative Algebra