\magnification=1200
\hsize=4in
\overfullrule=0pt
\input amssym
%\def\frac2{{#1\over #2}}
\def\emph#1{{\it #1}}
\def\em{\it}
\nopagenumbers
\noindent
%
%
{\bf John Talbot}
%
%
\medskip
\noindent
%
%
{\bf The Intersection Structure of $t$-Intersecting Families}
%
%
\vskip 5mm
\noindent
%
%
%
%
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.

\bye

.
