Abstract
LetC kn denote the set of allk-subsets of ann-set. AssumeA ⊆C a n and ℬ ⊆C b n . (A, ℬ) is called a cross-2-intersecting family if |A∩B|≥2 for anyA ∈ A,B ∈ ℬ.
In this paper, the best upper bounds of the cardinalities for non-empty cross-2-intersecting families ofa- andb- subsets are obtained for somea andb. A new proof for a Frankl-Tokushige theorem [6] is also given.
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Suppored by Postdoctral Fellowship Foundation of China.
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Shiquan, W. Non-empty cross-2-intersecting families of subsets. Appl. Math. 8, 175–181 (1993). https://doi.org/10.1007/BF02662001
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DOI: https://doi.org/10.1007/BF02662001