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From: riddle@emory.UUCP (Larry Riddle)
Newsgroups: sci.math
Subject: Re: A combinatorial problem: Do some n sets intersect?
Message-ID: <1951@emory.UUCP>
Date: Tue, 18-Nov-86 14:28:46 EST
Article-I.D.: emory.1951
Posted: Tue Nov 18 14:28:46 1986
Date-Received: Wed, 19-Nov-86 06:03:50 EST
References: <7978@watdaisy.UUCP>
Reply-To: riddle@emory.UUCP (Larry Riddle)
Distribution: sci
Organization: Math & Computer Science, Emory University, Atlanta
Lines: 24

Jan Pachl asked:

>> Let n be an integer, and let  A  be a collection
>> of  2n  sets.  Let  A  be closed under union (i.e. if two
>> sets belong to  A  then their union belongs to  A  as well).
>> Is it always true (i.e. for any  n  and any such  A ) that
>> some  n  sets in  A  intersect?
>> 
>> Apparently Erdos proposed the problem during one of his problem
>> talks, several years ago.  Is the problem recorded anywhere?
>> (If there is a solution, I'll take that, too).

I am passing on some information from a colleague.  Apparently Erdos
insists the problem did not originate with him.  Most people now credit
Peter Frankl, University of Paris.  The problem is still unsolved.
Ron Graham at one point thought he had a counterexample but it turned
out not to work.  My colleague says there are some partial results
known but did not know the details or references.

-- 
Larry Riddle        |  {akgua,sb1,gatech}!emory!riddle   USENET
Emory University    |  riddle@emory                      CSNET,BITNET
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