A****s
发帖数: 129 | 1 【 以下文字转载自 Quant 讨论区 】
发信人: Allens (ffff), 信区: Quant
标 题: a problem
发信站: BBS 未名空间站 (Mon Jan 18 21:16:40 2010, 美东)
Consider a cartesian product over n given finite sets,
X=X1×X2×。。。×Xn
Try to prove that X cannot be partitioned into less than 2^n subsets,
each of which is in form of Y1×Y2×。。。×Yn, Y1...Yn are proper subsets
of X1...Xn, respectively. | a***s
发帖数: 616 | 2 Since Y_i is a proper subset of X_i, to cover X_i we need at least one other
set Y_i^c = X_i \ Y_i.
【在 A****s 的大作中提到】
: 【 以下文字转载自 Quant 讨论区 】
: 发信人: Allens (ffff), 信区: Quant
: 标 题: a problem
: 发信站: BBS 未名空间站 (Mon Jan 18 21:16:40 2010, 美东)
: Consider a cartesian product over n given finite sets,
: X=X1×X2×。。。×Xn
: Try to prove that X cannot be partitioned into less than 2^n subsets,
: each of which is in form of Y1×Y2×。。。×Yn, Y1...Yn are proper subsets
: of X1...Xn, respectively.
| A****s
发帖数: 129 | 3 it's not a proof
other
【在 a***s 的大作中提到】
: Since Y_i is a proper subset of X_i, to cover X_i we need at least one other
: set Y_i^c = X_i \ Y_i.
| a***s
发帖数: 616 | 4 Do you mean it is wrong or it is not a complete proof?
【在 A****s 的大作中提到】
: it's not a proof
:
: other
| A****s
发帖数: 129 | 5 I think it is incomplete at the least. And I don't know whether you could
prove it from here.
【在 a***s 的大作中提到】
: Do you mean it is wrong or it is not a complete proof?
|
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