Maximum Hitting for n Sufficiently Large
Maximum Hitting for n Sufficiently Large
复制标题
n 足够大时的最大命中
DOI：
10.1007/s00373-012-1281-9
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发表时间：
2012
影响因子：
0.7
通讯作者：
Ben Barber
中科院分区：
文献类型：
--
作者：
Ben Barber
For a left-compressed intersecting family $${\fancyscript{A} \subseteq[n]^{(r)}}$$ and a set $${X \subseteq [n]}$$ , let $${\fancyscript{A}(X) = \{A \in \fancyscript{A} : A \cap X \neq \emptyset\}}$$ . Borg asked: for which X is $${|\fancyscript{A}(X)|}$$ maximised by taking $${\fancyscript{A}}$$ to be all r-sets containing the element 1? We determine exactly which X have this property, for n sufficiently large depending on r.
For a left-compressed intersecting family $${\fancyscript{A} \subseteq[n]^{(r)}}$$ and a set $${X \subseteq [n]}$$ , let $${\fancyscript{A}(X) = \{A \in \fancyscript{A} : A \cap X \neq \emptyset\}}$$ . Borg asked: for which X is $${|\fancyscript{A}(X)|}$$ maximised by taking $${\fancyscript{A}}$$ to be all r-sets containing the element 1? We determine exactly which X have this property, for n sufficiently large depending on r.