Geodesic
New bounds for union-free families of sets
The electronic journal of combinatorics, Tome 5 (1998)
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Following Frankl and Füredi 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 $$g(n) \leq 2^{[0.5+o(1)]n}.$$
DOI : 10.37236/1377
Classification : 05A10
Mots-clés : union-free families of sets 
@article{10_37236_1377,
     author = {Don Coppersmith and James B. Shearer},
     title = {New bounds for union-free families of sets},
     journal = {The electronic journal of combinatorics},
     year = {1998},
     volume = {5},
     doi = {10.37236/1377},
     zbl = {0906.05001},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1377/}
}
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Don Coppersmith; James B. Shearer. New bounds for union-free families of sets. The electronic journal of combinatorics, Tome 5 (1998). doi: 10.37236/1377

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