[seqfan] Re: need help calculating
davidsnewman at gmail.com
Sun May 19 22:46:39 CEST 2013
I should have written A 050342 in my previous post.
On Sun, May 19, 2013 at 7:49 PM, David Newman <davidsnewman at gmail.com>wrote:
> sequence A05342 asks for the number of partitions into "distinct parts"
> where each of the parts is itself a finite subset of the integers and the
> sum of the partition is the sum of all the integers in the set.
> What is the number of partitions of n if the sets are closed under union?
> For example: A05342 gives four partition of 4. Namely ( (4) ), ( (3,1)
> ) , ( (3), (1) ), ( (2,1), (1) )
> The third of these, ( (3), (1) ), would not be counted if we require that
> the sets be closed under union, since the union of the two singletons (3)
> and (1) is not an element of the partition.
> The idea of this sequence is from a famous conjecture by Frankl.
> The values that I've gotten so far are, for n=1,2,...,11 :
> 1,1,2,3,5,6,9,11, 15, 21 28
> I can't trust my hand computations and will be away from my copy of
> Mathematica until August.
> Anyone out there willing to verify and extend these numbers?
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