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{\bf John Talbot}
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{\bf The Intersection Structure of $t$-Intersecting Families}
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A family of sets is {\it $t$-intersecting} if any two sets from the
family contain at least $t$ common elements. Given a $t$-intersecting
family of $r$-sets from an $n$-set, how many distinct sets of size $k$
can occur as pairwise intersections of its members? We prove an
asymptotic upper bound on this number that can always be
achieved. This result can be seen as a generalization of the 
Erd\H os-Ko-Rado theorem.

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