Aldar C-F. Chan

2005-08-07 22:09:15 UTC

I have got the following problem. Does anybody know the

common methods used to solve this kind of problems? Or

where should I look up from?

Suppose I have a set X and partition it in different ways, say

P_1, P_2, ..., P_i,..., P_m. That is, each P_i is a distinct

partition of X. For any randomly selected subset of X, say

A \subset X, if I want to make sure X\A is equal to some

union of Y_i's where each Y_i is an element of the union of

P_1, ..., P_m. What is the minimum possible m for this to be

fulfilled? And how such a collection of partition patterns can

be found?

Thanks.

common methods used to solve this kind of problems? Or

where should I look up from?

Suppose I have a set X and partition it in different ways, say

P_1, P_2, ..., P_i,..., P_m. That is, each P_i is a distinct

partition of X. For any randomly selected subset of X, say

A \subset X, if I want to make sure X\A is equal to some

union of Y_i's where each Y_i is an element of the union of

P_1, ..., P_m. What is the minimum possible m for this to be

fulfilled? And how such a collection of partition patterns can

be found?

Thanks.