Several anzahl formulas of classical spaces and their applications

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• 作者：Jun Guo^a ; ^{guojun_lf@163.com" class="auth_mail} ; Fenggao Li^b ; ^{fenggaol@163.com" class="auth_mail}
• 关键词：05D05 ; 05E30
• 刊名：Linear Algebra and its Applications
• 出版年：15 July 2014
• 年：2014
• 卷：453
• 期：Complete
• 页码：154-173
• 全文大小：348 K

文摘

Let ${\mathbb{F}}_q^{2谓+未}$ be one of the (2谓+未)$(2谓+未)$-dimensional classical spaces and P   be a fixed subspace of type 蠎   of ${\mathbb{F}}_q^{2谓+未}$. Let M(i;蠎;m;2谓+未)$M(i;蠎;m;2谓+未)$ be the set of all m  -dimensional totally isotropic subspaces Q   of ${\mathbb{F}}_q^{2谓+未}$ satisfying dim(P∩Q)=i$\dim (P\cap Q)=i$. In this paper, we compute the size of M(i;蠎;m;2谓+未)$M(i;蠎;m;2谓+未)$ when P   is non-isotropic or totally isotropic. As applications, we give lower bounds of ranks of incidence matrices of totally isotropic subspaces of ${\mathbb{F}}_q^{2谓+未}$ over the real number field R$\mathbb{R}$, and compute eigenvalues of some graphs.