论文标题
正方形的伪羽毛图的EKR模块属性
The EKR-module property of pseudo-Paley graphs of square order
论文作者
论文摘要
我们证明，从环形类别的工会获得的平方顺序的伪paley图家族满足Erdős-ko-Rado（EKR）模块的特性，从某种意义上说，每个最大集团的特征向量是经典秘诀的特征性矢量的线性组合。这扩展了方顺序的Paley图的EKR模块特性，并解决了Godsil和Meagher提出的问题。与以前的作品不同，这些作品严重依赖数字理论的工具，我们的方法本质上纯粹是组合的。主要策略是将这些图视为正交阵列的块图，这是独立的。
We prove that a family of pseudo-Paley graphs of square order obtained from unions of cyclotomic classes satisfies the Erdős-Ko-Rado (EKR) module property, in a sense that the characteristic vector of each maximum clique is a linear combination of characteristic vectors of canonical cliques. This extends the EKR-module property of Paley graphs of square order and solves a problem proposed by Godsil and Meagher. Different from previous works, which heavily rely on tools from number theory, our approach is purely combinatorial in nature. The main strategy is to view these graphs as block graphs of orthogonal arrays, which is of independent interest.
