Data, Basudeb (1998) Pseudomanifolds with complementarity. In: Geometriae Dedicata, 73 (02). pp. 143-155.
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A simplicial complex is said to satisfy complementarity if exactly one of each complementary pair of nonempty vertex-sets constitutes a simplex of the complex. In this article we show that if there exists a n-vertex d-dimensional pseudo-manifold M with complementarity and either n less than or equal to d less than or equal to + 6 or d less than or equal to 6 then d = 0, 2, 4 or 6 with n = 3d/2 + 3. We also show that if M is a d-dimensional pseudo-manifold with complementarity and the number of vertices in M is less than or equal to d + 5 then M is either a set of three points or the unique 6-vertex real projective plane or the unique 9-vertex complex projective plane. Mathematics Subject Classification (1991): 57Q15.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to Springer.|
|Department/Centre:||Division of Physical & Mathematical Sciences > Mathematics|
|Date Deposited:||29 Dec 2009 08:31|
|Last Modified:||19 Sep 2010 05:26|
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