A multiply intersecting Erdos-Ko-Rado theorem - The principal case

@article{Tokushige2010AMI,
  title={A multiply intersecting Erdos-Ko-Rado theorem - The principal case},
  author={Norihide Tokushige},
  journal={Discrete Mathematics},
  year={2010},
  volume={310},
  pages={453-460}
}
Letm(n,k, r, t) be the maximum size of F ⊂ ([n] k ) satisfying|F1∩·· ·∩Fr | ≥ t for all F1, . . . ,Fr ∈ F . We prove that for everyp∈ (0,1) there is somer0 such that, for all r > r0 and allt with 1≤ t ≤ ⌊(p1−r − p)/(1− p)⌋− r, there existsn0 so that ifn > n0 and p = k/n, thenm(n,k, r, t) = (n−t k−t ) . The upper bound for t is tight for fixedp andr. 

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