On subspace arrangements of type \(\mathcal D\)
type: Item
instance of: scholarly article
title: On subspace arrangements of type \(\mathcal D\)
zbMATH Open document ID: 0965.52018
DOI: 10.1016/S0012-365X(99)00119-3
author: Eva-Maria Feichtner
author: Dmitry N. Kozlov
published in: Discrete Mathematics
publication date: 2001-07-30T00:00:00Z
review text: The subspace arrangements \({\mathcal D}_{n,k}\) formed by all subspaces of codimension \(k-1\) in \({\mathbb R}^n\) given by \(\varepsilon_1 x_{i_1}=\varepsilon_2x_{i_2}=\ldots=\varepsilon_k x_{i_k}\) for \(1\leq i_1 <i_2<\ldots < i_k\leq n\) and \(\varepsilon_j\in\{+1,-1\}\) are studied -- these turned out to be particularly interesting (difficult) examples in previous work by \textit{A. Björner} and \textit{B. Sagan} [J. Algebr. Comb. 5, 291-314 (1996; Zbl 0864.57031)]. The authors make considerable progress in the computation of the cohomology of the \({\mathcal D}_{n,k}\)-arrangements. For this they employ an arsenal of powerful tools, including \textit{D. Kozlov}'s method of EC-shellability [Ann. Comb. 1, 67-90 (1997; Zbl 0943.52004)] and a spectral sequence introduced by \textit{P. Hanlon} [Trans. Am. Math. Soc. 325, No. 1, 1-37 (1991; Zbl 0748.05043)].
Mathematics Subject Classification ID: 52C35
Mathematics Subject Classification ID: 52B22
Mathematics Subject Classification ID: 06A11
Mathematics Subject Classification ID: 05E25
zbMATH DE Number: 1389510
zbMATH Keywords: subspace arrangements
zbMATH Keywords: cohomology
zbMATH Keywords: shellability
zbMATH Keywords: spectral sequences
reviewed by: Günter M. Ziegler
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1389510