Saturating Sperner Families
Saturating Sperner Families
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斯佩纳家族饱和
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Balázs Patkós
中科院分区：
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作者：
Dániel Gerbner;Balázs Keszegh;N. Lemons;C. Palmer;Dömötör Pálvölgyi;Balázs Patkós
一个族$${mathcal{F}subseteq 2^{[n]}$$饱和了单调递减性质$${mathcal{P}}$$，如果$${mathcal{F}}$$满足$${mathcal{P}}$$，并且不能向$${mathcal{F}}$$添加任何集合，使得得到的族仍然满足$${mathcal{P}}$$。我们讨论了满足k-Sperner性质的族的最小规模和满足Sperner性质且仅由L集和(L)-集组成的族的最小规模问题。
A family $${mathcal{F} subseteq 2^{[n]}}$$ saturates the monotone decreasing property $${mathcal{P}}$$ if $${mathcal{F}}$$ satisfies $${mathcal{P}}$$ and one cannot add any set to $${mathcal{F}}$$ such that property $${mathcal{P}}$$ is still satisfied by the resulting family. We address the problem of finding the minimum size of a family saturating the k-Sperner property and the minimum size of a family that saturates the Sperner property and that consists only of l-sets and (l + 1)-sets.