j_jogar@yahoo.com science forum beginner
Joined: 14 Apr 2006
Posts: 1

Posted: Fri Apr 14, 2006 10:34 am Post subject:
combinatorial question



Let X={1,...,2n}.
Let P be the set of all partitions of X in n sets, that is,
P={P_1, ...,P_w}
where P_i is a partition of X in nsets (sets of cardinal n)
and w=S(2n,n) (the stirling number of second kind).
Let H={C_1, ..., C_z}, where for all i, C_i is an nsubset of X.
Suppose that for all P_i in P exists
C_j in H such that C_j is a crosssection for P_i.
I need a lower bound for z: for n big enough, and s=square root of 2n,
(2n)^s < z.
(but I ignore if this is true) 
