Normalized matching property of subspace posets in finite classical polar spaces

摘要

Let V be one of n-dimensional classical polar spaces over a finite field with q elements. Then all subspaces of V form a graded poset ordered by inclusion, denoted by P_n(q). Given a fixed maximal totally isotropic subspace P_o of V. Then each set P[t, P_0;n] = {Q ∈ p_n(q) | dim(Q ∩ P_0) ≥ t} is a graded subposet of P_n(q), where 0 ≤ t ≤ v -1. In this paper we show that P[t, P_0; n] has the NM property, which implies that V[t, P_0; nl has the strong Sperner property and the LYM property.