l The maximum weight of cross-t intersecting families
Speaker
l Sang June Lee
Date
l 2013-02-21
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l The Arithmetic of Function Fields and Related Topics (2. 18~21)
A central result in extremal combinatorics is textit{the ErdH os--Ko--Rado Theorem} which investigates the maximum size of $cA subset binom{[n]}{k}$ such that for every choice of sets $A_1, A_2in cA$ we have $|A_1cap A_2| geq t$. In this talk we consider a version with two families. Two families $cA$ and $cB subset binom{[n]}{k}$ are {em cross $t$-intersecting} if for every choice of sets $A in cA$ and $B in cB$ we have $|A cap B| geq t$. The following `cross $t$-intersecting version' of the ErdH os-Ko-Rado Theorem was conjectured: For all $n geq (t+1)(k-t+1)$ the maximum value of $|cA||cB|$ for two cross $t$-intersecting families $cA, cB subsetbinom{[n]}{k}$ is $binom{n-t}{k-t}^2$.We verified a strongly related textit{$p$-weighted version} of the above conjecture for $t geq 14$. For $0
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