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Pseudomanifolds with Complementarity
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A simplicial complex is said to satisfy complementarity if exactly one of each complementary pair of nonempty vertexsets constitutes a simplex of the complex. In this article we show that if there exists a nvertex ddimensional pseudomanifold M with complementarity and either n≤d+6 or d≤ 6 then d = 0, 2, 4 or 6 with n = 3d/2 + 3. We also show that if M is a ddimensional pseudomanifold with complementarity and the number of vertices in M is ≤ d+5 then M is either a set of three points or the unique 6vertex real projective plane or the unique 9vertex complex projective plane.
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 Title
 Pseudomanifolds with Complementarity
 Journal

Geometriae Dedicata
Volume 73, Issue 2 , pp 143155
 Cover Date
 19981101
 DOI
 10.1023/A:1005076308582
 Print ISSN
 00465755
 Online ISSN
 15729168
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 pseudomanifolds
 triangulation
 complementarity.
 Industry Sectors
 Authors

 Basudeb Data ^{(1)}
 Author Affiliations

 1. Department of Mathematics, Indian Institute of Science, Bangalore, 560 012, India; email