论文信息 - Families of finite sets in which no set is covered by the union ofr others

Families of finite sets in which no set is covered by the union ofr others

AbstractLetfr(n, k) denote the maximum number ofk-subsets of ann-set satisfying the condition in the title. It is proved that $$f_1 (n,r(t - 1) + 1 + d)\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } (_{ t}^{n - d} )/(_{ t}^{k - d} )$$ wheneverd=0, 1 ord≦r/2t2 with equality holding iff there exists a Steiner systemS(t, r(t−1)+1,n−d). The determination offr(n, 2r) led us to a new generalization of BIBD (Definition 2.4). Exponential lower and upper bounds are obtained for the case if we do not put size restrictions on the members of the family.

P. Erdös | P. Frankl | Z. Füredi

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