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Link complexes of subspace arrangements
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2007 (English)In: European journal of combinatorics (Print), ISSN 0195-6698, E-ISSN 1095-9971, Vol. 28, no 3, 781-790 p.Article in journal (Refereed) Published
Abstract [en]

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 R. 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 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.

Place, publisher, year, edition, pages
2007. Vol. 28, no 3, 781-790 p.
Keyword [en]
coloring complex, graph, polynomials
URN: urn:nbn:se:kth:diva-16456DOI: 10.1016/j.ejc.2005.12.006ISI: 000244966900012ScopusID: 2-s2.0-33751414068OAI: diva2:334498
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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Hultman, Axel
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