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{\bf Don Coppersmith and James B. Shearer}
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{\bf New Bounds for Union-free Families of Sets}
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Following Frankl and F{\"u}redi we say a family, $F$, of subsets of an
$n$-set is weakly union-free if $F$ does not contain four distinct sets
$A$, $B$, $C$, $D$ with $A \cup B = C \cup D$. If in addition
$A \cup B = A \cup C$ implies $B=C$ we say $F$ is strongly union-free.
Let $f(n)$ ($g(n)$) be the maximum size of strongly (weakly) union-free
families. In this paper we prove the following new bounds on $f$ and $g$:
$$2^{[0.31349+o(1)]n} \leq f(n) \leq 2^{[0.4998+o(1)]n}$$ and
$$g(n) \leq 2^{[0.5+o(1)]n}.$$
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