Elsevier

Discrete Mathematics

Volume 58, Issue 2, February 1986, Pages 191-193
Discrete Mathematics

Note
Explicit construction of exponential sized families of k-independent sets

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Abstract

Error correcting codes are used to describe explicit collections Fk of subsets of {1,2,...;n}, with |Fk| > 2ck·n (Ck > 0), such that for any selections A, B of k2 and k1 of members of Fk with k1 + k2 = k, there are elements in all the members of A and not in the members of B. This settles a problem of Kleitman and Spencer and a similar problem of Kleimman, Shearer and Sturtevant.

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Research supported in part by the Weizmann Fellowship for Scientific Research