论文信息 - An identity in combinatorial extremal theory

An identity in combinatorial extremal theory

Abstract Our main discovery is the following identity: For every family A ⊂ 2 Ω of non-empty subsets of Ω = {1, 2, …, n} ∑ X⊂ω W A (X) ∥X∥( n X ) ≡1 where W A (X)=| ⋂ X⊃AϵA A|. It can be viewed as a sharpening of the famous LYM-inequality. We present also generalizations to other posets. The total impact for combinatorics remains to be explored. The identity seems to be particularly useful for uniqueness proofs in Sperner Theory. We also discuss a geometric consequence.

Rudolf Ahlswede | R. Ahlswede | Zhen Zhang | Zhen Zhang

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