On subspace arrangements of type \(\mathcal D\) (Q1961245)

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)].