Normalized matching property of a class of subspace lattices (Q2470788)

The paper generalizes Lih' theorem for subspaces of a finite vector space in the following manner: let \(V_n(q)\) be the \(n\)-dimensional vector space over the \(q\)-element finite field. Let \(K\) be a fixed \(k\)-dimensional subspace of it. Finally let \(C[n,k,t]\) be the subspaces of \(V_n(q)\) intersecting \(K\) in a subspace of at least \(t\)-dimension (\(t\) is fixed arbitrarily within \([1,k]\)). The paper proves that \(C[n,k,t]\) satisfies the normalized matching property, therefore it has the strong Sperner property.