On subspace arrangements of type

Let Dn,k denote the subspace arrangement formed by all linear subspaces in Rn given by equations of the formε1xi1=ε2xi2=⋯=εkxik,where 1⩽i1<⋯n/2. Moreover, we prove that H̃i(Πn,k±)=0 unless i≡n−2 (mod k−2) or i≡n−3 (mod k−2), and that H̃i(Πn,k±) is free abelian for i≡n−2 (mod k−2). In the special case of Π2k,k± we determine homology completely. Our tools are generalized lexicographic shellability, as introduced in Kozlov (Ann. Combin. 1 (1997) 67–90), and a spectral sequence method for the computation of poset homology first used in Hanlon (Trans. Amer. Math. Soc. 325 (1991) 1–37).