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A family A of ‘-element subsets and a family B of k-element subsets of an n-element set are cross-intersecting if every set from A has a nonempty intersection with every set from B. We compare two(More)
For a Sperner family A ⊆ 2 [n] let Ai denote the family of all i-element sets in A. We sharpen the LYM inequality i |Ai|/ n i ≤ 1 by adding to the LHS all possible products of fractions |Ai|/ n i ,(More)