论文标题
模块化和分数L相反的矢量空间家族
Modular and fractional L-intersecting families of vector spaces
论文作者
论文摘要
在本文的第一部分中，我们证明了一个定理，它是[Alon，Babai，Suzuki，J。Combin所示的广义模块化雷 - chaudhuri-wilson定理的$ q $ analogue。理论系列A，1991年]。它也是[Frankl and Graham，欧洲J. Combin中的主要定理的概括。 [1985]在某些情况下。 在本文的第二部分中，我们在最近的一个概念上证明了$ q $ - nalogues的结果，称为\ emph {分数$ l $ -intersecting family}，用于给定矢量空间的子空间家庭。我们使用上述定理获得与此类家庭基数的一般上限。在某些特殊情况下，我们对这一一般上限进行了改进。
In the first part of this paper, we prove a theorem which is the $q$-analogue of a generalized modular Ray-Chaudhuri-Wilson Theorem shown in [Alon, Babai, Suzuki, J. Combin. Theory Series A, 1991]. It is also a generalization of the main theorem in [Frankl and Graham, European J. Combin. 1985] under certain circumstances. In the second part of this paper, we prove $q$-analogues of results on a recent notion called \emph{fractional $L$-intersecting family} for families of subspaces of a given vector space. We use the above theorem to obtain a general upper bound to the cardinality of such families. We give an improvement to this general upper bound in certain special cases.
