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Pairs of disjoint q-element subsets far from each other ∗†

By Hikoe Enomoto and Gyula O. H. Katona


Let n and q be given integers and X a finite set with n elements. The following theorem is proved for n> n0(q). The family of all q-element subsets of X can be partitioned into disjoint pairs (except possibly one if ( n) q is odd), so that |A1 ∩ A2 | + |B1 ∩ B2 | ≤ q, |A1 ∩ B2 | + |B1 ∩ A2 | ≤ q holds for any two such pairs {A1, B1} and {A2, B2}. This is a sharpening of a theorem in [2]. It is also shown that this is a coding type problem, and several problems of similar nature are posed.

Year: 2012
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