Abstract
A family 
of ℓ-element subsets and a family 
of k-element subsets of an n-element set are cross-intersecting if every set from has a nonempty intersection with every set from . We compare two previously established inequalities each related to the maximization of the product 
, and give a new and short proof for one of them. We also determine the maximum of 
for arbitrary positive weights ωℓ,ω
k
.
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Bey, C. On Cross-intersecting Families of Sets. Graphs and Combinatorics 21, 161–168 (2005). https://doi.org/10.1007/s00373-004-0598-4
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DOI: https://doi.org/10.1007/s00373-004-0598-4