论文标题
erdős-ko-rado定理和双线性形式的矩阵，用于残基类环上的矩阵
Erdős-Ko-Rado theorem and bilinear forms graphs for matrices 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 $。令$ 1 \ leq r \ leq m \ leq n $和$ \ mathbb {z} _ {h}^{m \ times n} $是所有$ m \ times n $矩阵的集合。 $ \ mathbb {z} _ {h} $上的概括性双线性形式图，由$ \ hbox {bil} _r（\ Mathbb {z} _ {h} _ {h}^{m \ times n}）$表示，有山顶$ \ m m i} $ {z} _ {m {h}如果内部排名$ a-b $小于或等于$ r $，则顶点$ a $ a $ a $ a $和$ b $相邻。在本文中，我们确定了$ \ hbox {bil} _r（\ mathbb {z} _ {h}^{m \ times n}）$的$ \ hbox {bil} _r（\ mathbb {z} _r的最大群集的总数和几何结构。结果，获得了$ \ mathbb {z} _h^{m \ times 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 $1\leq r\leq m\leq n$ and $\mathbb{Z}_{h}^{m\times n}$ be the set of all $m\times n$ matrices over $\mathbb{Z}_{h}$. The generalized bilinear forms graph over $\mathbb{Z}_{h}$, denoted by $\hbox{Bil}_r(\mathbb{Z}_{h}^{m\times n})$, has the vertex set $\mathbb{Z}_{h}^{m\times n}$, and two distinct vertices $A$ and $B$ are adjacent if the inner rank of $A-B$ is less than or equal to $r$. In this paper, we determine the clique number and geometric structures of maximum cliques of $\hbox{Bil}_r(\mathbb{Z}_{h}^{m\times n})$. As a result, the Erdős-Ko-Rado theorem for $\mathbb{Z}_h^{m\times n}$ is obtained.
