Cameron-Liebler Line Classes, Tight Sets and Strongly Regular Cayley Graphs

发布时间：2022-03-21 作者：浏览次数：

Speaker:	向青	DateTime:	2022年03月19日（周六）上午：10:00-11:00
Brief Introduction to Speaker: 向青，讲席教授。研究领域包括组合设计、有限几何、编码理论和加法组合。1995年毕业于俄亥俄州立大学，获博士学位。1999年获得国际组合数学及其应用协会颁发的Kirkman奖章。曾任美国加州理工学院Bateman Instructor, 美国特拉华（Delaware）大学终身教职，和浙江大学讲座教授。现为南方科技大学讲席教授。		Place:	腾讯会议号：417-720-663
Abstract: Abstract：Cameron-Liebler line classes are sets of lines in ${\rm PG}(3,q)$ having many interesting combinatorial properties. These line classes were first introduced by Cameron and Liebler in their study of collineation groups of ${\rm PG}(3,q)$ having the same number of orbits on points and lines of ${\rm PG}(3,q)$. During the past decade, Cameron-Liebler line classes have received considerable attention from researchers in both finite geometry and algebraic combinatorics. In the original paper \cite{camlie} by Cameron and Liebler, the authors gave several equivalent conditions for a set of lines of ${\rm PG}(3,q)$ to be a Cameron-Liebler line class; later Penttila gave a few more of such characterizations. We will use one of these characterizations as the definition of Cameron-Liebler line class. Let ${\mathcal L}$ be a set of lines of ${\rm PG}(3,q)$ with $\|L\|=x(q^2+ q+1)$, $x$ a positive integer. We say that ${\mathcal L}$ is a Cameron-Liebler line class with parameter $x$ if...

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