partition of a set - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T18:56:30Z http://mathoverflow.net/feeds/question/21060 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/21060/partition-of-a-set partition of a set mingming 2010-04-12T02:18:43Z 2010-04-12T02:27:58Z <p>First, we see this example. Suppose we have a set of 6 elements, we can get 3 subsets of it, each of which has 2 elements, but no two sets overlap. But if our set has 5 elements, we want to get 3 subsets of it each of which has 2 elements . Then two of them need to overlap on 1 element. Now generally suppose we have a set of #a elements and we want 3 subsets of it each of which has #a' elements. We also want each two of them have the same but least # in common. Could you get the relationship between a and a'? How many does any two of them in common? How many does three of them has in common? For example, if a=3a', the we can have no pair of the three subsets overlap.</p> http://mathoverflow.net/questions/21060/partition-of-a-set/21061#21061 Answer by Gerhard Paseman for partition of a set Gerhard Paseman 2010-04-12T02:27:58Z 2010-04-12T02:27:58Z <p>You might try the problem for dividing a set into two sets first, and explore the possibilities. For working with three sets, I like to visualize the set as evenly distributed around a circle, with the subsets covering certain arcs of the circle. Perhaps this visualization will help you.</p> <p>Gerhard "Ask Me About System Design" Paseman, 2010.04.11</p>