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.