Normalized matching property of subspace posets in finite classical polar spaces

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 Pn(q). Given a fixed maximal totally isotropic subspace P0 of V. Then each set P[t,P0;n]={Q∈Pn(q)|dim(Q∩P0)⩾t} is a graded subposet of Pn(q), where 0⩽t⩽ν−1. In this paper we show that P[t,P0;n] has the NM property, which implies that P[t,P0;n] has the strong Sperner property and the LYM property.