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{\bf Geoffrey McKenna}
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{\bf Sunflowers in Lattices}
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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.

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