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 P-n(q). Given a fixed maximal totally isotropic subspace P-0 of V. Then each set P[t, P-0; n] = {Q is an element of P-n(q) vertical bar dim(Q boolean AND 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 P[t, P-0; n] has the strong Sperner property and the LYM property. (c) 2012 Elsevier Inc. All rights reserved.