53 research outputs found
Union-intersecting set systems
Three intersection theorems are proved. First, we determine the size of the
largest set system, where the system of the pairwise unions is l-intersecting.
Then we investigate set systems where the union of any s sets intersect the
union of any t sets. The maximal size of such a set system is determined
exactly if s+t4. Finally, we exactly determine
the maximal size of a k-uniform set system that has the above described
(s,t)-union-intersecting property, for large enough n.Comment: 9 page
Two-part and k-Sperner families: New proofs using permutations
This is a paper about the beauty of the permutation method. New and shorter proofs are given for the theorem [P. L. Erdős and G. O. H. Katona, J. Combin. Theory. Ser. A,4
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