Link complexes of subspace arrangements

Details Link complexes of subspace arrangements Link complexes of subspace arrangements

2005-07-15

arxiv.org/abs/math/0507314v2

Mathematics

Combinatorics

10 pages; updated reference for Theorem 4.1 (thanks to E. Delucchi)

Scientific paper

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.

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