A product version of the Erd?s-Ko-Rado theorem

摘要

Let F_1,...,F_r?(~([n])_k) be r-cross t-intersecting, that is, |F_1∩..F_r|≥t holds for all F_1∈F_1,...,F_r∈F_r. We prove that for every p,μ∈(0,1) there exists r_0 such that for all r>r_0, all t with 1≤t<(1/p-μ)~(r-1)/(1-p)-1, there exist n_0 and ∈ so that if n>n_0 and |k-p|<∈, then |F_1|··· |F_r|≤(~(n-t)_(k-t))r.