\magnification=1200
\hsize=4in
\overfullrule=0pt
\input amssym
%\def\frac#1 #2 {{#1\over #2}}
\def\emph#1{{\it #1}}
\def\em{\it}
\nopagenumbers
\noindent
%
%
{\bf Geoffrey McKenna}
%
%
\medskip
\noindent
%
%
{\bf Sunflowers in Lattices}
%
%
\vskip 5mm
\noindent
%
%
%
%
A Sunflower is a subset $S$ of a lattice, with the property that the
meet of any two elements in $S$ coincides with the meet of all of
$S$. The Sunflower Lemma of Erd\"os and Rado asserts that a set of
size at least $1 + k!(t-1)^k$ of elements of rank $k$ in a Boolean
Lattice contains a sunflower of size $t$.  We develop counterparts of
the Sunflower Lemma for distributive lattices, graphic matroids, and
matroids representable over a fixed finite field.  We also show that
there is no counterpart for arbitrary matroids.

\bye

.