报告人：侯新民副教授中国科学技术大学
报告题目：Maximal fractionalcross-intersecting families
报告时间：2022年4月16日（周六）下午14:00
报告地点：腾讯会议（会议ID：515-443-656）
主办单位：数学与统计学院、科学技术研究院
报告人简介：
侯新民，中国科学技术大学数学科学学院，副教授，博士生导师。感兴趣研究领域包括结构图论、极值图论、组合优化等，已发表学术论文60余篇，主持完成国家自然科学基金4项，省部级项目2项。
报告摘要：
Given an irreducible fraction $\frac{c}{d}\in [0,1]$, a pair $(\mathcal{A},\mathcal{B})$ is called a$\frac{c}{d}$-cross-intersecting pair of $2^{[n]}$ if $\mathcal{A},\mathcal{B}$ are two families of subsets of $[n]$ such that for every pair $A\in\mathcal{A}$ and $B\in\mathcal{B}$, $|A \cap B|= \frac{c}{d}|B|$. Mathew,Ray, and Srivastava [{\it\small Fractional cross intersecting families, Graphsand Comb., 2019}] proved that $|\mathcal{A}||\mathcal{B}|\le 2^n$ if$(\mathcal{A}, \mathcal{B})$ is a $\frac{c}{d}$-cross-intersecting pair of$2^{[n]}$ and characterized all the pairs $(\mathcal{A},\mathcal{B})$ with$|\mathcal{A}||\mathcal{B}|=2^n$, such a pair also is called a maximal $\fraccd$-cross-intersecting pair of $2^{[n]}$, when $\frac cd\in\{0,\frac12, 1\}$.In this talk, we characterize all the maximal $\frac cd$-cross-intersectingpairs $(\mathcal{A},\mathcal{B})$ when $0<\frac{c}{d}<1$ and $\frac cd\not=\frac12$, this result answers a question proposed by Mathew, Ray, and Srivastava(2019).