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Let D n,k denote the subspace arrangement formed by all linear subspaces in R n given by equations of the form 1 x i1 = 2 x i2 =...= k x ik ,where 1=<i 1 <...<i k =<n and ( 1 ,..., k ) {+1,-1} k .Some important topological properties of such a subspace arrangement...
Loeb et al. (J. Combin. Theory. Ser A. 65 (1994) 151-157) gave an explicit semisymmetric chain decomposition of Π(n). In this paper we give a second explicit semisymmetric chain decomposition and show that it is different from the one given in Loeb et al. (1995) in the sense that no order automorphism of Π(n) can carry one to another.
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