Normalized matching property of a class of subspace lattices

Abstract

Let Vn(q) be the n-dimensional vector space over the finite field with q elements and K a selected k-dimensional subspace of V n(q). Let C[n, k, t] denote the set of all subspaces S's such that dim(S ∩ K) ≥ t. We show that C[n, k, t] has the normalized matching property, which yields that C[n, k, t] has the strong Sperner property and the LYM property.