论文标题
erdős-ko-rado定理，用于残留类环上的矢量空间
Erdős-Ko-Rado theorem for vector spaces over residue class rings
论文作者
论文摘要
令$ h = \ prod_ {i = 1}^{t} p_i^{s_i} $是将其分解为独特的素数的产物，$ \ mathbb {z} _ {h} _ {h} $是残基类别rang rand ring modulo $ h $。令$ \ mathbb {z} _ {h}^{n} $为$ n $ -dimensional Row vector Space上的$ \ Mathbb {z} _ {h} $。 $ \ mathbb {z} _ {h}^n $的广义Grassmann图，由$ g_r（m，n，\ mathbb {z} _ {h} _ {h}）$（简称为$ g_r $），所有$ m $ -m $ -subspaces of $ \ subspaces of $ \ \ \ \ \ \ \ \ \ \ \ s iTs at iTs and as as as as as as as as as at iTs相邻如果它们的交叉点为尺寸$> m-r $，其中$ 2 \ leq r \ leq m+1 \ leq n $。在本文中，我们确定了$ g_r $的最大集团的总数和几何结构。结果，我们获得了$ \ mathbb {z} _ {h}^{n} $的erdős-ko-rado定理。
Let $h=\prod_{i=1}^{t}p_i^{s_i}$ be its decomposition into a product of powers of distinct primes, and $\mathbb{Z}_{h}$ be the residue class ring modulo $h$. Let $\mathbb{Z}_{h}^{n}$ be the $n$-dimensional row vector space over $\mathbb{Z}_{h}$. A generalized Grassmann graph for $\mathbb{Z}_{h}^n$, denoted by $G_r(m,n,\mathbb{Z}_{h})$ ($G_r$ for short), has all $m$-subspaces of $\mathbb{Z}_{h}^n$ as its vertices, and two distinct vertices are adjacent if their intersection is of dimension $>m-r$, where $2\leq r\leq m+1\leq n$. In this paper, we determine the clique number and geometric structures of maximum cliques of $G_r$. As a result, we obtain the Erdős-Ko-Rado theorem for $\mathbb{Z}_{h}^{n}$.
