作者PttFund (批踢踢基金只进不出)
看板Math
标题[离散] 离散(2)
时间Sun Jul 24 16:49:21 2005
Suppose F is a family of subsets of { 1, 2, ..., n } such that
A does not contains B and B does not contains A for any two
distinct A, B in F.
n
Prove that |F|≦( ). Moreover, prove that if equality holds,
└n/2┘
then F consists of all subsets of { 1, 2, ..., n } of size └n/2┘,
or all subsets of size ┌n/2┐ (these are the same if n is even).
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