[離散] 離散(2)

[PttFund (批踢踢基金只進不出)]

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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我好窮啊，我好缺批幣啊
，你有摳摳ㄋㄟ
可憐可憐我吧，施捨一點吧
請到(P)LAY-->(P)AY-->(0)GIVE-->PttFund-->吧

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