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- W2953283804 abstract "A pair of families $(cF,cG)$ is said to be emph{cross-Sperner} if there exists no pair of sets $F in cF, G in cG$ with $F subseteq G$ or $G subseteq F$. There are two ways to measure the size of the pair $(cF,cG)$: with the sum $|cF|+|cG|$ or with the product $|cF|cdot |cG|$. We show that if $cF, cG subseteq 2^{[n]}$, then $|cF||cG| le 2^{2n-4}$ and $|cF|+|cG|$ is maximal if $cF$ or $cG$ consists of exactly one set of size $lceil n/2 rceil$ provided the size of the ground set $n$ is large enough and both $cF$ and $cG$ are non-empty." @default.
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- W2953283804 date "2011-04-20" @default.
- W2953283804 modified "2023-09-27" @default.
- W2953283804 title "Cross-Sperner families" @default.
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