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COMBINATORICS
1998

New Bounds for Union-free Families of Sets

13 years 3 months ago
New Bounds for Union-free Families of Sets
: Following Frankl and F¨uredi [1] 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 ∪ B = C ∪ D. If in addition A ∪ B = A ∪ 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 ≤ f(n) ≤ 2[0.4998+o(1)]n and g(n) ≤ 2[0.5+o(1)]n . AMS Subject Classification. 05B10
Don Coppersmith, James B. Shearer
Added 21 Dec 2010
Updated 21 Dec 2010
Type Journal
Year 1998
Where COMBINATORICS
Authors Don Coppersmith, James B. Shearer
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