an:00599877
Zbl 0798.05071
Ruszink??, Mikl??s
On the upper bound of the size of the \(r\)-cover-free families
EN
J. Comb. Theory, Ser. A 66, No. 2, 302-310 (1994).
00020352
1994
j
05D05 94B25
upper bound; \(r\)-cover-free families; superimposed code; set compression algorithm
Let \(T(r,n)\) denote the maximum number of subsets of an \(n\)-set such that no subset is covered by the union of any other \(r\) subsets (such a system is called \(r\)-cover-free). It is shown that for \(n\) sufficiently large
\[
{\log_ 2 T(r,n)\over n}\leq 8 {\log_ 2 r\over r^ 2}.
\]
This comes from a better understanding and proof of a result of A. G. Dyachkov and V. V. Rykov. The central element of this proof is a new set compression algorithm.
P.L.Erd??s (Almare)