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发布日期:2020-12-01点击量:

报告题目:Cameron-Liebler line classes and Two-Intersection Sets

报告人:向青 讲席教授 (南方科技大学)

报告时间:2020年12月4日下午16:00-17:00

报告地点:

摘要:Cameron-Liebler line classes are sets of lines in $\PG(3,q)$ having many interesting combinatorial properties. These line classes were first introduced by Cameron and Liebler in their study of collineation groups of $\PG(3,q)$ having the same number of orbits on points and lines of $\PG(3,q)$. During the last decade, Cameron-Liebler line classes have received considerable attention from researchers in both finite geometry and algebraic combinatorics. In the original paper by Cameron and Liebler, the authors gave several equivalent conditions for a set of lines of $\PG(3,q)$ 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 $\PG(3,q)$ with $|{\mathcal L}|=x(q^2+q+1)$, $x$ a nonnegative integer. We say that ${\mathcal L}$ is a Cameron-Liebler line class with parameter $x$ if every spread of $\PG(3,q)$ contains $x$ lines of ${\mathcal L}$. It turned out that Cameron-Liebler line classes are closely related to certain two-intersection sets in $\PG(5,q)$.

We will talk about a recent construction of a new infinite family of Cameron-Liebler line classes with parameter $x=\frac{(q+1)^2}{3}$ for $q\equiv 2\pmod{3}$. When $q$ is an odd power of $2$, this family of Cameron-Liebler line classes represents the first infinite family of Cameron-Liebler line classes ever constructed in $\PG(3,q)$, $q$ even. This talk is based on joint work with Tao Feng, Koji Momihara, Morgan Rodgers and Hanlin Zou.



联系人:张俊

主办单位:首都师范大学数学科学学院、万博体育max手机登陆app-手机版下载