combinatorial question

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

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 n-sets (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 n-subset of X.

Suppose that for all P_i in P exists
C_j in H such that C_j is a cross-section 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)

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