Abstract
Let ℋ be an arrangement of n hyperplanes in Pd, C(ℋ) its cell complex, and H any hyperplane of ℋ. It is proved: (1) If ℋ is not a near pencil then there are at least n−d−1 simplicial d-cells of C(ℋ), each having no facet in H. (2) There are at least d+1 simplicial d-cells of C(ℋ), each having a facet in H.
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