Abstract
Let n i, k i be positive integers, i=1, ..., d,satisfying n i≥2k i. Let X 1, ..., X d be pairwise disjoint sets with | X i| =n i. Let H be the family of those ( k 1+···+k d)- element sets which have exactly k i elements in X i, i=1,..., d. It is shown that if F ⊂ H is an intersecting family then | F |/| H |≤ max ik i/n i, and this is best possible. The proof is algebraic, although in the d=2 case a combinatorial argument is presented as well.
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