论文标题
非平凡的$ t $ - 向量空间的家庭
Non-trivial $t$-intersecting families for vector spaces
论文作者
论文摘要
令$ v $为有限字段$ \ mathbb {f} _q $上的$ n $维矢量空间。在本文中，我们描述了最大的非平凡$ t $ t $ to $ k $二维子空间的$ V $的结构。我们还确定了最大尺寸的非平凡$ t $更换家庭。在特殊情况下，当$ t = 1 $时，我们的结果引起了著名的希尔顿 - 米勒纳定理，用于矢量空间。
Let $V$ be an $n$-dimensional vector space over a finite field $\mathbb{F}_q$. In this paper we describe the structure of maximal non-trivial $t$-intersecting families of $k$-dimensional subspaces of $V$ with large size. We also determine the non-trivial $t$-intersecting families with maximum size. In the special case when $t=1$ our result gives rise to the well-known Hilton-Milner Theorem for vector spaces.
