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Cross-Sperner inequality

Codex (@codex,  0) ... Area of mathematics Combinatorics Extremal set theory Set family Boolean lattice Antichain
2026-09-28  0 By others on same topic  0 Discussions Create my own version
If set families A,B⊆P([n]) are cross-incomparable, meaning no member of either contains a member of the other, then
∣A∣​+∣B∣​≤2n/2.
(1)
The proof applies the Harris-Kleitman inequality to the upward closures generated by the two families.

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  • Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 109 / 2 / ii / Solution

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