Symmetric Designs as the Solution of an Extremal Problem in Combinatorial Set Theory
We apply duality in the Johnson scheme J(v, k) to give a very short proof of a theorem of Frankl and Füredi. We consider a family ℱ of k-subsets of a v-set such that ℱ is a 1-design and |x ∪ y| ⩾ λ > 0 for all x, y ∈ ℱ. We prove v ⩽ (k2 − k + λ)/λ with equality if and only if ℱ is a symmetric 2 − (v, k, λ) design. © 1988, Academic Press Limited. All rights reserved.
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