Explicit construction of exponential sized families of k-independent sets

@article{Alon1986ExplicitCO,
  title={Explicit construction of exponential sized families of k-independent sets},
  author={Noga Alon},
  journal={Discrete Mathematics},
  year={1986},
  volume={58},
  pages={191-193}
}
A collection F of subsets of N = {1, 2 , . . . , n} is k i n d e p e n d e n t if for every k distinct members A 1, A2 , • • • , A k of F all 2 k intersections Ak=l Bj are nonempty, where each Bj can be either Aj or its complement Aj. Kleitman and Spencer [4] proved that for every fixed k there exists a k-independent collection F k on n elements of size 1>2 ckn, where Ck > 0 is independent of n. Their proof is nonconstructive, i.e., it gives no explicit construction of such an F k. They thus… CONTINUE READING
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