Combinatorial manifolds with complementarity
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چکیده
Abstract. A simplicial complex is said to satisfy complementarity if exactly one of each complementary pair of nonempty vertex-sets constitutes a face of the complex. We show that if a d-dimensional combinatorial manifold M with n vertices satisfies complementarity then d = 0, 2, 4, 8 or 16 with n = 3d/2 + 3 and IMI is a "manifold like a projective plane". Arnoux and Marin had earlier proved the converse statement.
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