Erdős theorem on k-Sperner families
= Erdős theorem on k-Sperner families
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Among $k$-Sperner subfamilies of $\mathcal P([n])$, the maximum cardinality is the sum of the $k$ largest <binomial coefficients> $\binom nj$. The union of the corresponding levels attains the bound. For the upper bound, the <Lubell mass> is at most $k$, and assigning its available mass to the levels with largest binomial coefficients maximizes cardinality.