Constructing union-free pairs of k-element subsets
نویسنده
چکیده
It is proved that one can choose ⌊ 1 2 ( n k )⌋ disjoint pairs of k-element subsets of an n-element set in such a way that the unions of the pairs are all different, supposing that n > n(k).
منابع مشابه
An Upper Bound on the Sizes of Multiset-Union-Free Families
Let F1 and F2 be two families of subsets of an n-element set. We say that F1 and F2 are multiset-union-free if for any A,B ∈ F1 and C,D ∈ F2 the multisets A ⊎ C and B ⊎D are different, unless both A = B and C = D. We derive a new upper bound on the maximal sizes of multiset-union-free pairs, improving a result of Urbanke and Li.
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تاریخ انتشار 2012