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1-04吴文俊数学重点实验室组合图论系列讲座之129【刘西之】
报告题目:Conditionally Intersecting Families

报告人:刘西之 (Department of Mathematics, Statistic and Computer Science,University of Illinois at Chicago)

时间:1月4日(周五)上午 10:30-11:30

地点:1418

摘要:
Let $k\ge d\ge 2$ be fixed. Let $\mathcal{F}$ be a family of k-sets of [n]. $\mathcal{F}$ is (d,s)-conditionally intersecting if it does not contain d sets whose union is of size at most s and empty intersection. The celebrated Erd\H{o}s-Ko-Rado theorem states that if $n\ge 2k$, then a (2,2k)-conditionally intersecting family $\mathcal{F}$ has size at most $\binom{n-1}{k-1}$. Mubayi conjectured that if $n\ge dk/(d-1)$, then a (d,2k)-conditionally intersecting family $\mathcal{F}$ also has size at most $\binom{n-1}{k-1}$. Lots of efforts were devoted into the study of this conjecture in the recent dacade. In this talk, I will discuss a further sharpen of Mubayi's conjecture. In particular, I will talk about the upper bound for a (d,2k)-conditionally intersecting family $\mathcal{F}$ with matching number at least $\nu$. Our result settles a conjecture of Mommoliti and Britz. This is joint work with Dhruv Mubayi.
  科大主页 | 国家数学与交叉科学中心(合肥) | 中科院吴文俊数学重点实验室 |
中科院数学与系统科学研究院 | 北京国际数学研究中心 | 安徽省数学会