youngman
证明: 将N个对象随机分配到两个组中, 当两组中对象个数相同时, 组合数达到最大.
此题本人很长时间没有头绪, 如各位大虾给出证明或很好的提示, 即给本版送上经典书籍: Alan Agresti Categorical data analysis (2nd edition) 电子版. 谢谢.
rtist
好像很简单啊?似乎直接展开就可以看到的啊?
(2n choose m)=C(2n choose n) for 0<=m<=n
where C can be factorized as (n-m) factors, with each btwn 0 & 1.
Hence 0<C<1.
youngman
请问btwn是什么含义, 另外C的展开能不能说的详细点, 本人初学, 请见谅.
rtist
btwn is short for between.
just write out the factorials explicitly and you can see it easily after some cancellation.
dwt1981
推荐用归纳法试试,嘿嘿!
dwt1981@yahoo.com.cn,谢谢啊!
招摇撞骗就是我
rtist
[quote]引用第4楼dwt1981于2007-07-04 21:16发表的“”:
招摇撞骗就是我[/quote]
这句话什么意思?
youngman
谢谢,不过请问如果证明了0<C<1, 是否还需要证明C是最小的才能保证组合数最大呢?
rtist
[quote]引用第6楼youngman于2007-07-05 08:33发表的“”:
谢谢,不过请问如果证明了0<C<1, 是否还需要证明C是最小的才能保证组合数最大呢?[/quote]
No, because m is ANY interger btwn 0 and n. That is, for any m satisfying this mild condition, there exists such a C that is btwn 0 and 1. This is enough to finish the proof.