2022. 11. 24. 12:30 - 2022. 11. 24. 14:00
Rényi, Nagyterem + Zoom
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Esemény típusa: szeminárium
Szervezés: Intézeti
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Extremális halmazrendszerek szeminárium

Leírás

Abstract:

We will introduce the paper written by Wenjun Yu, Xiangliang Kong, Yuanxiao Xi, Xiande Zhang and Gennian Ge.

In order to generalize Turán number to hypergraphs, Bollobás proved the following well-known theorem which is named Bollobás-type theorem today:
Suppose that $(A_i,B_i)$ is a collection of pairs of sets which satisfied cross-inersecting condition.
Then we have
\begin{equation}
\sum_{i}\frac{1}{{|A_i|+|B_i|}\choose{A_i}}\leq 1.
\end{equation}
In particular, if all of the $A_i$'s have the same cardinal number $a$, and all of the $B_i$'s have cardinal number $b$, then the maximum size of the collection is ${a+b}\choose{a}$.
Using an amazing algebraic method, in 1977, Lovász proved that similar result is true for vector spaces.
In 1984, Füredi generalized both of the theorems (for sets and for vector spaces) to the case of the threshold version, or in other words, the $t-intersecting$ version.

In this talk, we will follow a recent reseach, and consider the case of hemi-bundled two families. Specifically, on the premise of the (threshold) cross-intersecing condition, what can we say if we further suppose that one of the two families of sets in Bollobás-type theorem is an intersecting family. And we will also appreciate how Lovász's graceful exterior product method works in these combinatorics problems.

 

The lecture can be followed by zoom: