A NEW GENERALIZATION OF TIIE ERDIS - KO - RADO THEOREM 3 . The proof of Theorem 3

Abstract

-. L9t F_be a family of-k-subsets of an rr-set. Let s be a fixed integer satisfying k<s=3k. Suppose that for Fl,F2,&€g lp'uaunl=s implies FanFze|4#g. katona asktd what is the maximum cardinality, Í'@,k,s'} of such a system. The Erdős-Ko-Rado theorem implies /-_1\ Ív'k,s):[í-iJ "' s:3k and n=2k. Inthis paper we show that f (n,k'"):Íí:1lholdsfor nrno(k) if and only if s>2k. Equality holds only if every nrember of F contains a fixed element of the underlying set. Furtherwesolvetheproblemfor k:3,s:-5,n=3000. Thisresultsharpensatheoremof Bo||obás.

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@inproceedings{Frankl1983ANG, title={A NEW GENERALIZATION OF TIIE ERDIS - KO - RADO THEOREM 3 . The proof of Theorem 3}, author={Liselotte Frankl and Z . FUREDT}, year={1983} }