Abstract
Let ℱ be a family of subsets of a finite set ofn elements. The vector (f 0, ...,f n ) is called the profile of ℱ wheref i denotes the number ofi-element subsets in ℱ. Take the set of profiles of all families ℱ satisfyingF 1⊄F 2 andF 1∩F 2≠0 for allF 1,F 2teℱ. It is proved that the extreme points of this set inR n+1 have at most two non-zero components.
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Dedicated to Paul Erdős on his seventieth birthday