
학 술 대 회 명 
l Colloquium at Yonsei University 

강 연 주 제 
l An ErdosKoRado Theorem for cross $t$intersecting families 

발 표 년 도 
l 2013 

발 표 월 
l 05 

저 자 
l Lee, Sang June 

개 최 국 가 
l 대한민국 

다운로드 
l
1363158445_0.53486.pdf


Abstract:
(Also, see the attached file.)
A central result in extremal set theory is the extit{ErdH osKoRado Theorem} (1961) which investigates the maximum size of families $mathcal{A} subset biom{[n]}{k}:={Ssubset [n] : S=k}$ such that for every choice of $A_1, A_2in mathcal{A}$ we have $A_1cap A_2 geq t$.
Two families $mathcal{A}, mathcal{B}subset biom{[n]}{k}:={Ssubset [n] : S=k}$ are {em cross $t$intersecting} if for every choice of subsets $A in mathcal{A}$ and $B in mathcal{B}$ we have $A cap B geq t$.
The following was conjectured as the cross $t$intersecting version of
the ErdH osKoRado Theorem: For all $tgeq 1$, $kgeq t$ and $n geq (t+1)(kt+1)$, the maximum value of $mathcal{A}mathcal{B}$ for two cross $t$intersecting families $mathcal{A}, mathcal{B} subset binom{[n]}{k}$ is $binom{nt}{kt}^2$.
In this talk we verify this for $t geq 14$, large enough $k$
(depending on $t$ and any $delta>0$), and $n geq (t+1+delta)k$. Note that this range of $n$ is arbitrarily close to $ngeq (t+1)(kt+1)$ in the conjecture if $delta$ is small and $k$ is large. Our proofs make use of a {em weight} version of the problem and {em randomness}.
This is joint work with Peter Frankl, Norihide Tokushige, and Mark Siggers. 



