Non-empty cross-3-intersection theorems of subsets
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Maximum families of subsets satisfying some specified conditions are widely studied in combinatorics on set systems. In this paper, an extremal problem on subsets is considered. Let C n k denote the set of all k-subsets of an n- set. Assume A ⊂ C n a and B ⊂ C n b , (A B) is called a cross-t-intersecting family if ¦ A ∩ B ¦≥ t for any A ∈ A, B ∈ B. For t=3, maximum non-empty cross-3-intersecting families of a- and b- subsets are obtained.
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