Pseudomanifolds with complementarity (Q1275280)

A finite simplicial complex has complementarity if exactly one of each pair of complementary sets of vertices spans a simplex. The author shows that if a \(d\)-dimensional simplicial pseudo-manifold with complementarity has \(n\) vertices and \(n\leq d+6\) or \(d\leq 6\), then \(d=0,2,4\), or 6 and \(n=3d/2+3\). The author goes on to determine all \(d\)-dimensional simplicial pseudo-manifolds with complementarity and fewer than \(d+6\) vertices.