Non-empty cross-3-intersection theorems of subsets
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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