Abstract
Solomon showed that the Poincare polynomial of a Coxeter group W satisfies a product decomposition depending on the exponents of W. This polynomial coincides with the rank-generating function of the poset of regions of the underlying Coxeter arrangement. In this note we determine all instances when the analogous factorization property of the rank-generating function of the poset of regions holds for a restriction of a Coxeter arrangement. It turns out that this is always the case with the exception of some instances in type $$E_8$$.
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